Hi friends, thanks so much for watching this video! A kind viewer has pointed out that I have got my signs mixed up a bit! The drag force, which should indeed be acting in the opposite direction to the sine component of the gravitational force, already has an in-built negative sign due to the angular velocity (at least at the position the pendulum is in in our diagram). Therefore, the third term in the equation at 10:07 should actually be positive (unless we were to say that gamma is negative). Whoops :D Thanks Murillo for pointing out my error! Thank you all once again for watching, please do check out my classical physics playlist for more videos like this: ua-cam.com/play/PLOlz9q28K2e7UlSbJIwYTtR77CLmV5_3z.html
I want a video on how do we see things around us?? As we say that light is reflected from that objects to our eyes but why don't the light Rays interact in space as so many waves from all directions are crossing each other.. How these lights retain special information about shape size of any object.. Please answer ..🙏🙏🙏🙏
It would be nice if you could explain why simple pendulum liked in science museums (with extremely long string) never stop oscillating. Is it the gravitational force make it to overcome the air drag?
The drag force is not opposite the gravitational force at all times. When the pendulum is swinging “down” or towards the center, the drag and gravity are opposite. But when the pendulum is swinging “up” both gravity and drag are pulling in the same direction. The sign is negative (in your video’s original notation) not because it’s opposite gravity but because it’s opposite in direction to the velocity.
@@windowsxseven Wow, imagine being this much of a jerk for no reason. You could have just not written that and the world would have been a little better.
I would love to see a video about solving basic differential equations(not numerically) or building uderstanding of a certain process by simply looking at them.
@@amritkumarpatel5717 Thanks, but i am aware that numerical differentiation is not necessarily that hard, but i am not really satisfied with this, i would like to solve this without programing. And I have also learnt basic calculus. 1st class in high school.
unfortunately differential equations like these are reaaally far off from being considered basic so if you want to just go with the basic ones just study integration with rectilinear motion
I am a retired US Navy veteran Aircraft Structures, Airframes, Hydraulics, Pneumatics Flight Controls Systems Technician and I have always wanted to know the advanced physics and math those Mechanical and Aeronautical Engineers know. I have been looking for an answer, for this simple pendulum problem and I have hanged string bob pendulums in my garage at STP 'Standard Temperature and Pressure' and have watched many excellent lectures here on UA-cam, my mathematical physics or math can only grasp college algebra, basic physics and trigonometry with some knowledge of calculus one. Finally I have found your VIDEO gave me the insight in the way you have explained this complex problem. My goal was to know how to derive the real world mathematical physics of THE TIME 't', when the pendulum swinging has practically STOPPED, in air as a Mechanical Engineering problem. Thank You SIR. AWESOME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!......
Great to see vids like this up so thank you, but I'm unsure of some of your assumptions. You state that drag force is proportional to velocity, but I believe that is damping force that is proportional to the speed something moves, however, air resistance/drag is proportional to velocity^2. What you're including in your model is frictional damping (proportional to velocity, or in this case angular velocity), which would give a different differential equation and solution at the end if this difference was taken into account.
For small bodies and low speeds the drag force is proportional to velocity but for large speeds like that of an airplane the drag force is proportional to velocity squared.
4:00 The accepted unit for angular velocity (speed) is radians per sec, rad/s, not degrees per second, where pi radians are equal to 180 degrees (1 rad = 57.3 degrees). The reason for using radians instead of degrees is that it allows us to relate angular quantities to linear quantities by multiplying by the radius. displacement = radius x angular displacement; velocity = radius x angular velocity; acceleration = radius x angular acceleration, and so on.
Hey man .I love your explaintion .smoth explaintion .I want see your vedio but now I can't because my jee exam is after months .but after exam I definitely going to whatch lots of your vedio .my emence love for physics ❤️.
9:50 At low speeds the drag is proportional to the velocity, at higher speeds it is proportional to the square of the velocity. For instance, an automobile driving along a road at 60 MPH (miles per hour) experiences a drag four times the drag it would experience at 30 MPH. On the other hand, the drag you experience walking at 6 MPH would only be twice the drag you would when walking at 3 MPH.
I've been waiting for a video like that for a long time. Thank you yt suggestions! But I need to know one more thing: IS AIR RESISTANCE ACTUALLY DIRECTLY PROPORTIONAL TO THE SPEED OF THE PENDULUM IN A LINEAR MANNER?
well is more accurate to say that is proportional to the SQUARE of the velocity. The linear is more accurate when the fluid surrounding the "experiment" (in this case the air) is behaving like a laminar fluid, which is not the case, but it is better than assuming not air resistance at all
Hello sir, I see you haven't made a video on small angle approximation of theta, please make a video on it if you can, your way of explanation makes me love physics, thank you
It isn't that complicated. You notice in his diagram that up to about 30 degrees the sine curve is very close to linear, so we just assume it is linear and that allows us to use the angle instead the sine of the angle. Mathematically sine is defined by the Taylor Series sin(x) = x − x^3/3! + x^5/5! - x^7/7! + ... (the denominators are factorials, 3! = 1x2x3, 5! = 1x2x3x4x5) x is measured in radians, where pi radians is equal to 180 degrees. For small angles, the effect of the second, third fourth and higher terms is small enough to be ignored. In fact, at 30 degrees the sine = 0.5, and the angle in radians is 0.5236 That's about a 4.5% difference. Think back to the 1951 version of "The Day the Earth Stood Still" 😄😆 BARNHARDT: You wrote this? KLAATU: It was a clumsy way to introduce myself -- but I understand you're a difficult man to see. I thought you'd have the solution by this time. BARNHARDT: Not yet. That's why I wanted to see you. KLAATU: All you have to do now is substitute this expression-- (pointing to a specific place) --at this point. BARNHARDT: Yes -- that will reproduce the first-order terms. But what about the effect of the other terms? KLAATU: Almost negligible... With variation of parameters, this is the answer. BARNHARDT: How can you be so sure? Have you tested this theory? KLAATU: (with a slight smile) I find it works well enough to get me from one planet to another. (Barnhardt stares at him blankly)
Hey Parth, can you make a video on how to get into Cambridge as an international student? and will you be willing to collab with a fan on a future physics-based project if it interests you? Love the content keep up the good work.
something greate to see is that aire resistancee doesn´t change the pendulum´s frequency, so you can calculate gravity with a pendulum in anywhere even when there is air resistance.
This is jus amazing 😍 Everything I've learnt so far(about this topic ofc lol), fall directly into pieces, and you love to see it! You're jus the best teach.
Hi Parth! Love your videos. How do you do your animations? My girlfriend is a chemistry teacher and would like to create something similar for her class.
To be fair, there is good reason to ignore air resistance from a pedagogical perspective. In a lot of cases resistance makes the maths harder, sometimes intractably so? without really changing the underlying phenomenon. You don't need to understand air resistance to understand an awful lot of classical mechanics. Additionally, the inclusion of air resistance often doesn't change numerical answers all that much - but even when it does, understanding a phenomenon without air resistance is a prerequisite to the refinement of including air resistance anyway, so it's still a necessary first step.
Isnt this another simplification when making the velocity dependence linear? Especially for really small/large velocities when in reality the damping should be lower/higher than a mass-spring-model predicts?
2:00 Terminal velocity is often misunderstood leading to silly situations in movies and TV shows where writers have people falling out of fiftieth floor windows hitting the ground higher speed (greater impact) than say tenth floor windows. You might also hear stupid statements like he fell from 5,000 feet as if the person will hit the ground at a higher speed than falling from 100 feet, for example.
You have two issues with your explanation that I think are of critical importance to understand the equation. At 8:45 you say that the force due to drag is directly proportional to the speed of the pendulum and point out d(theta)/dt, this is right. However, at 9:05 you say that the drag force is acting in the opposite direction to the gravitational force which is only true part of the time. When the pendulum is at a maximum height and falling, gravity is pulling the pendulum down and speeding it up but drag is acting in the opposite direction of the velocity of the pendulum trying to slow it down. As the pendulum passes through the mid-point at the bottom, gravity is now slowing the pendulum and has a component acting in the SAME direction as drag. It is important to be clear on this as the gravity term is dependent upon theta while drag is dependent upon d(theta)/dt. Physically and conceptually these are very different. Secondly, you say that the negative sign means that drag is acting in the opposite direction as gravity which isn't true about the negative sign. The negative sign means that the drag is acting in the opposite direction as d(theta)/dt, not gravity or theta explicitly (which gravity is explicitly dependent upon). Making this distinction is important as the direction of force due to gravity is dependent upon what side of the bottom (mid-point) the pendulum is at (that is, it changes mid swing), while the force due to drag is dependent upon the direction of travel and thus is in the same direction during one complete swing from one side to the other. As a result, the periodic back and forth motion is purely driven by gravity while the dampening of the amplitude is purely caused by drag. Edit: On a side note, I do enjoy your videos and think you do a great job.
Drag is strange. Sometimes it's modelled as proportional to speed, sometimes as proportional to the square of speed and real strange things happen over 80% the speed of sound. I kinda wonder whar would happen to pendulum if drag was proportional to square of speed, but for low speeds this solution looks close enough.
Thank you so much Sir. From 🇿🇦 SA Though I have to confess I had to Replay 5times to understand as I was distracted at the first two attempts by the looks on the left hand side no offence 🙏 never the less I finally Overstrand now. thank you.
Hey Parth. I finalised my concept of damping with this superb video. But, I think, u forgot to divide 'γ' (proportionality constant) by 'm' (mass of bob) in the final Differential Equation; as otherwise, it will clearly show the dimensional incorrectness with other terms of the Differential Equation. Once again, thanks for your superb content...👍👍
Important distinction! The drag force is only proportional to the speed (1st power) for slow laminar flow. This is not the case for air, which is always turbulent. Then the force is proportional to the speed squared, but that introduces non-linear dynamics which are really cumbersome and usually solved numerically - so I understand why you chose the former, but even though it is a drag force, it's not really air resistance :-)
Hi, when looking for work done by air resistance, say for example there is a constant air resistance force of 5N acting on a ball that is connected to a string. The string is 4m long and is held at a 90 degree angle parallel to the ground. It is then dropped down and falls in a circular motion due to the tension of the string. Work = Force x distance of displacement. So would the distance of displacement be equal to the angular displacement? or would the displacement be equal to 4 since it goes from a height of 4 meters to 0 meters? The 4 meters coming from the 4m long radius of the circle (string).
Parth I want a video on how do we see things around us?? As we say that light is reflected from that objects to our eyes but why don't the light Rays interact in space as so many waves from all directions are crossing each other.. How these lights retain special information about shape size of any object.. Please answer ..
What is A and B... did I miss that? (I guess that A and B must have something to do with L ang g) Is the frequency the same no mater the drag force?, since it is outside the cos and sin part of the equation?
By convention, we use angles up to 10 degrees for our small angle approximation, but 60 degrees is far beyond the acceptable limit. Did you misspeak and say 60 degrees when you meant 6 degrees?
Consider that the pendulum is at rest with θ_0>0, measured counterclockwise. When the motion starts, pendulum acquires angular velocity dθ/dt in the clockwise sense. So dθ/dt0, we have: F_gravitational = -g/L*θ
For sure, you're right! One could model the aerodynamic drag with a force with magnitude equal to Cd*ρ*V²*A/2, where Cd is the drag coefficient (that may also vary with the Reynolds number of the flow). That would produce an non linear ODE that is hard to be analytically solved, as presented below. d2θ/dt2 + γ*(dθ/dt)² + g/L*θ = 0 Of course it is possible to solve this equation numerically, but the reason to model the drag force as a linear function of the speed is only to simplify the calculations, once the ODE obtained is linear and can be easliy solved: d2θ/dt2 + γ*dθ/dt + g/L*θ = 0
Great video. One question, how do you go about finding gamma and is the density of the medium the only factor in finding it or does it also involve other things like the incident area of the mass?
And would you actually calculate gamma for the value of air resistence?! Could please make a video deepening a little bit more about the matter...?! Please!!! This is quite interesting!!!
Can you pls explain or make video on time period of a vertical circular motion for a Bob attached to a string.(for minimum condition which is at top the speed of Bob is square root of rg where r is radius and g acceleration due to gravity) I am not even able to get the formula anywhere on the net or books forget about the derivation. Pls help
Minor constructive comment: maybe you could have mentioned that the small angle approximation only works if the angle is given in radians. As you were talking about the approximation being valid up to 60 degrees some confusion may have been caused.
Not necessarily. Drag force can act both proportional to v and v^2 depending on whether it is laminar or turbulent in nature. The drag equation you mentioned assumes that an object is moving at a high enough velocity to have a high enough reynolds number to assume turbulent flow. This isn't necessarily the case with the pendulum.
8:20 The solution to a second order differential (it has a second derivative) like this, is a function with a second derivative equal to the negative of the original function. Sine is a solution because the derivative of sine is cosine, and the derivative of cosine is negative sine. We can also write the sine as a function of exponentials and find an exponential solution, but that is too difficult for this video.
make sense but how more far we can push that padular effect.. i'm stuck on that theory since 2005 involving money... & energy & connaissance. because my boss stole my idea. and integrated in is business process.. and there internal security service have a part of is system on the same taxe credits that is buit the structural of it... can you develop ??????
it would stop and float only if the drag force was equal to the weight of the object the moment it has 0 velocity. But when it is equalized at a certain time when it has (u) downward velocity there will be no net force to decelerate it (ΣF=ma=0)
"Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (190 km/h or 118 mph) for a human skydiver."
triggered engineer here. did you just use the small angle approximation for angles up to 60 degrees? we get shit from the mathematicians and physicists for using it up to 5 degrees in some circumstances. that's ridiculous.
Hi friends, thanks so much for watching this video! A kind viewer has pointed out that I have got my signs mixed up a bit! The drag force, which should indeed be acting in the opposite direction to the sine component of the gravitational force, already has an in-built negative sign due to the angular velocity (at least at the position the pendulum is in in our diagram). Therefore, the third term in the equation at 10:07 should actually be positive (unless we were to say that gamma is negative). Whoops :D
Thanks Murillo for pointing out my error!
Thank you all once again for watching, please do check out my classical physics playlist for more videos like this: ua-cam.com/play/PLOlz9q28K2e7UlSbJIwYTtR77CLmV5_3z.html
I thought the sign changes because of the rearrangement of the terms to the RHS of the eqn
I want a video on how do we see things around us??
As we say that light is reflected from that objects to our eyes but why don't the light Rays interact in space as so many waves from all directions are crossing each other..
How these lights retain special information about shape size of any object..
Please answer ..🙏🙏🙏🙏
Plzzz make a video on reversible and irreversible process in thermodynamics
It would be nice if you could explain why simple pendulum liked in science museums (with extremely long string) never stop oscillating. Is it the gravitational force make it to overcome the air drag?
The drag force is not opposite the gravitational force at all times. When the pendulum is swinging “down” or towards the center, the drag and gravity are opposite. But when the pendulum is swinging “up” both gravity and drag are pulling in the same direction. The sign is negative (in your video’s original notation) not because it’s opposite gravity but because it’s opposite in direction to the velocity.
Could you please explain "Natural Frequency" of objects to us? Thank you!
he probably could but doesn't want to
@@windowsxseven Wow, imagine being this much of a jerk for no reason. You could have just not written that and the world would have been a little better.
@@pairot01 wtf u on about mate it’s not his fault if he doesn’t want to make a video on it
@@pairot01 he just said he might want not to make the video and you do that, prick.
For Those who don't want to go deep but also want to know the "other related" quantity, it's torque. Which is kinda angular force.
I would love to see a video about solving basic differential equations(not numerically) or building uderstanding of a certain process by simply looking at them.
I have learnt basic calculus . Differentiation numerically Is not that hard that u are thinking. Which grade are u in.
@@amritkumarpatel5717 Thanks, but i am aware that numerical differentiation is not necessarily that hard, but i am not really satisfied with this, i would like to solve this without programing. And I have also learnt basic calculus. 1st class in high school.
@@przemekreszka2825 ooo noice. I am in 7th
unfortunately differential equations like these are reaaally far off from being considered basic so if you want to just go with the basic ones just study integration with rectilinear motion
@@przemekreszka2825 ua-cam.com/video/efvT2iUSjaA/v-deo.html
here you go, Papa flammy does that stuff
Huge fan sir from 🇳🇵Nepal
Ma ni nepal bata🥰🥰
Me too 🇳🇵
Same here
Nepal must be great.. greetings from the much lower alps in austria ;-)
Greetings from your southern bretheren!
I am a retired US Navy veteran Aircraft Structures, Airframes, Hydraulics, Pneumatics Flight Controls Systems Technician and I have always wanted to know the advanced physics and math those Mechanical and Aeronautical Engineers know.
I have been looking for an answer, for this simple pendulum problem and I have hanged string bob pendulums in my garage at STP 'Standard Temperature and Pressure' and have watched many excellent lectures here on UA-cam, my mathematical physics or math can only grasp college algebra, basic physics and trigonometry with some knowledge of calculus one. Finally I have found your VIDEO gave me the insight in the way you have explained this complex problem. My goal was to know how to derive the real world mathematical physics of THE TIME 't', when the pendulum swinging has practically STOPPED, in air as a Mechanical Engineering problem. Thank You SIR. AWESOME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!......
Thanks Parth for this amazing content, I always wanted this as a high schooler but didn't find any good video.
Thank you
Is he of Indian origin
Because if he is I'm really proud of him ..
@@nitd955 yes
You explain so well and I, as many others, don't feel anxious listening and learning, a BRILLIANT teacher, thank you very very much!
Love your videos very much Parth. Can you tell what was your thesis about?
Yup..
Eagerly waiting to know
Great Brother...
May I know what was your thesis?
01:25, my dog in essence, tastes drag force everytime i drive.
Great to see vids like this up so thank you, but I'm unsure of some of your assumptions. You state that drag force is proportional to velocity, but I believe that is damping force that is proportional to the speed something moves, however, air resistance/drag is proportional to velocity^2. What you're including in your model is frictional damping (proportional to velocity, or in this case angular velocity), which would give a different differential equation and solution at the end if this difference was taken into account.
For small bodies and low speeds the drag force is proportional to velocity but for large speeds like that of an airplane the drag force is proportional to velocity squared.
4:00 The accepted unit for angular velocity (speed) is radians per sec, rad/s, not degrees per second, where pi radians are equal to 180 degrees (1 rad = 57.3 degrees). The reason for using radians instead of degrees is that it allows us to relate angular quantities to linear quantities by multiplying by the radius. displacement = radius x angular displacement; velocity = radius x angular velocity; acceleration = radius x angular acceleration, and so on.
This is the perfect youtuber for me...
Mrbeast, Pewdiepie etc.
Are just show offs. He is the real person
Thanks bro..
Don't you dare talk about mr beast he isn't what you think
Lol what are u comparing bro they both create completely different content
@@jayamalinir8011 Ya Mr. Beast is love tho I have stopped watching pewds now .
Hey man .I love your explaintion .smoth explaintion .I want see your vedio but now I can't because my jee exam is after months .but after exam I definitely going to whatch lots of your vedio .my emence love for physics ❤️.
9:50 At low speeds the drag is proportional to the velocity, at higher speeds it is proportional to the square of the velocity. For instance, an automobile driving along a road at 60 MPH (miles per hour) experiences a drag four times the drag it would experience at 30 MPH. On the other hand, the drag you experience walking at 6 MPH would only be twice the drag you would when walking at 3 MPH.
I've been waiting for a video like that for a long time. Thank you yt suggestions! But I need to know one more thing: IS AIR RESISTANCE ACTUALLY DIRECTLY PROPORTIONAL TO THE SPEED OF THE PENDULUM IN A LINEAR MANNER?
well is more accurate to say that is proportional to the SQUARE of the velocity. The linear is more accurate when the fluid surrounding the "experiment" (in this case the air) is behaving like a laminar fluid, which is not the case, but it is better than assuming not air resistance at all
Hello Parth! Your videos encourage me to learn something new everyday. Suggestion: Please make a video on string theory.
"Real Physics"
Physicists: *TRIGGERED*
Engineers: : )
Hello sir, I see you haven't made a video on small angle approximation of theta, please make a video on it if you can, your way of explanation makes me love physics, thank you
It isn't that complicated. You notice in his diagram that up to about 30 degrees the sine curve is very close to linear, so we just assume it is linear and that allows us to use the angle instead the sine of the angle.
Mathematically sine is defined by the Taylor Series
sin(x) = x − x^3/3! + x^5/5! - x^7/7! + ... (the denominators are factorials, 3! = 1x2x3, 5! = 1x2x3x4x5)
x is measured in radians, where pi radians is equal to 180 degrees.
For small angles, the effect of the second, third fourth and higher terms is small enough to be ignored. In fact, at 30 degrees the sine = 0.5, and the angle in radians is 0.5236 That's about a 4.5% difference.
Think back to the 1951 version of "The Day the Earth Stood Still" 😄😆
BARNHARDT: You wrote this?
KLAATU: It was a clumsy way to introduce myself -- but I understand you're a difficult man to see. I thought you'd have the solution by this time.
BARNHARDT: Not yet. That's why I wanted to see you.
KLAATU: All you have to do now is substitute this expression-- (pointing to a specific place) --at this point.
BARNHARDT: Yes -- that will reproduce the first-order terms. But what about the effect of the other terms?
KLAATU: Almost negligible... With variation of parameters, this is the answer.
BARNHARDT: How can you be so sure? Have you tested this theory?
KLAATU: (with a slight smile) I find it works well enough to get me from one planet to another.
(Barnhardt stares at him blankly)
Damnnn, you explained it so gently, I was surprised I could follow to the end with ease. 😁
Superb Video !
What Software Do yo use for your animations ?
would be nice to see two examples calculated one without drag and one with drag good vid thanks
Would love to see the pendulum+air resistance done via Lagrangian mechanics.
please cover the brachistochrone
Hey guess what, a similar question to brachistochrone was asked once in JEE Advanced.
Your videos are very informative respect from🇮🇳 India ...
By the way do you have any connection with India ..
As you look Indian???
Nice explained video Parth... You make the world of physics more explained well and that makes me happier
.. Thanks and stay safe of Covid19... Parth
Hey Parth, can you make a video on how to get into Cambridge as an international student?
and will you be willing to collab with a fan on a future physics-based project if it interests you?
Love the content keep up the good work.
change your name to Ramanujan, make really awesome discoveries in maths and a professor named hardy will invite you to Cambridge, ez pz
something greate to see is that aire resistancee doesn´t change the pendulum´s frequency, so you can calculate gravity with a pendulum in anywhere even when there is air resistance.
Good job...a video with maths and physics. Might start watching again as some earlier videos were good but not for the physics buff.
This is jus amazing 😍
Everything I've learnt so far(about this topic ofc lol), fall directly into pieces, and you love to see it! You're jus the best teach.
Bro is he of Indian origin
Hi Parth! Love your videos. How do you do your animations? My girlfriend is a chemistry teacher and would like to create something similar for her class.
To be fair, there is good reason to ignore air resistance from a pedagogical perspective. In a lot of cases resistance makes the maths harder, sometimes intractably so? without really changing the underlying phenomenon. You don't need to understand air resistance to understand an awful lot of classical mechanics.
Additionally, the inclusion of air resistance often doesn't change numerical answers all that much - but even when it does, understanding a phenomenon without air resistance is a prerequisite to the refinement of including air resistance anyway, so it's still a necessary first step.
Isnt this another simplification when making the velocity dependence linear? Especially for really small/large velocities when in reality the damping should be lower/higher than a mass-spring-model predicts?
Excellent talk !
Simple is always good. Things should never be told complicated. Thank you.
Good video! Although I understand the mathematics but it's no clear why drag depends of velocity...
Does size have any effect on air resistance... Like how big or small the object in question is?
2:00 Terminal velocity is often misunderstood leading to silly situations in movies and TV shows where writers have people falling out of fiftieth floor windows hitting the ground higher speed (greater impact) than say tenth floor windows. You might also hear stupid statements like he fell from 5,000 feet as if the person will hit the ground at a higher speed than falling from 100 feet, for example.
cool video parth!! i suggest maybe natural frequency in the future? thank you!!
You have two issues with your explanation that I think are of critical importance to understand the equation. At 8:45 you say that the force due to drag is directly proportional to the speed of the pendulum and point out d(theta)/dt, this is right. However, at 9:05 you say that the drag force is acting in the opposite direction to the gravitational force which is only true part of the time. When the pendulum is at a maximum height and falling, gravity is pulling the pendulum down and speeding it up but drag is acting in the opposite direction of the velocity of the pendulum trying to slow it down. As the pendulum passes through the mid-point at the bottom, gravity is now slowing the pendulum and has a component acting in the SAME direction as drag. It is important to be clear on this as the gravity term is dependent upon theta while drag is dependent upon d(theta)/dt. Physically and conceptually these are very different. Secondly, you say that the negative sign means that drag is acting in the opposite direction as gravity which isn't true about the negative sign. The negative sign means that the drag is acting in the opposite direction as d(theta)/dt, not gravity or theta explicitly (which gravity is explicitly dependent upon). Making this distinction is important as the direction of force due to gravity is dependent upon what side of the bottom (mid-point) the pendulum is at (that is, it changes mid swing), while the force due to drag is dependent upon the direction of travel and thus is in the same direction during one complete swing from one side to the other. As a result, the periodic back and forth motion is purely driven by gravity while the dampening of the amplitude is purely caused by drag.
Edit: On a side note, I do enjoy your videos and think you do a great job.
Loved the video Parth. You made it so easy.
Drag is strange. Sometimes it's modelled as proportional to speed, sometimes as proportional to the square of speed and real strange things happen over 80% the speed of sound. I kinda wonder whar would happen to pendulum if drag was proportional to square of speed, but for low speeds this solution looks close enough.
Second year physics undergrad here, definitely a good refresher!
U literally explained the damped free vibration concept....😀
Thank you so much Sir. From 🇿🇦 SA
Though I have to confess I had to Replay 5times to understand as I was distracted at the first two attempts by the looks on the left hand side no offence 🙏 never the less I finally Overstrand now. thank you.
exactly what I was looking for, thank you.
Hey Parth. I finalised my concept of damping with this superb video.
But, I think, u forgot to divide 'γ' (proportionality constant) by 'm' (mass of bob) in the final Differential Equation; as otherwise, it will clearly show the dimensional incorrectness with other terms of the Differential Equation.
Once again, thanks for your superb content...👍👍
Love from India ❤️❤️
Important distinction! The drag force is only proportional to the speed (1st power) for slow laminar flow. This is not the case for air, which is always turbulent. Then the force is proportional to the speed squared, but that introduces non-linear dynamics which are really cumbersome and usually solved numerically - so I understand why you chose the former, but even though it is a drag force, it's not really air resistance :-)
Hi, when looking for work done by air resistance, say for example there is a constant air resistance force of 5N acting on a ball that is connected to a string. The string is 4m long and is held at a 90 degree angle parallel to the ground. It is then dropped down and falls in a circular motion due to the tension of the string. Work = Force x distance of displacement. So would the distance of displacement be equal to the angular displacement? or would the displacement be equal to 4 since it goes from a height of 4 meters to 0 meters? The 4 meters coming from the 4m long radius of the circle (string).
I have a test tomorrow and would greatly appreciate a response before then 😅
Parth I want a video on how do we see things around us??
As we say that light is reflected from that objects to our eyes but why don't the light Rays interact in space as so many waves from all directions are crossing each other..
How these lights retain special information about shape size of any object..
Please answer ..
Ignoring *air resistance* is like *altering* constant *pi* with 22/7, just because you're dealing with *multiple of 7*
finally a useful video
Hi Parth, Are You an Indian? Your Videos are Great.
Please make video on quantum fluctuations (quantum foam..)
Great video and simply explained
We were taught damping oscillations back in 9th grade but never like this! Great vid.
Is he of Indian origin..
@@nitd955 no idea
@@arpitbisht3228 ya he is from mumbaiii.....
And he shifted to UK in 2005.
I saw an old video
Parth and please share your thesis
What is A and B... did I miss that?
(I guess that A and B must have something to do with L ang g)
Is the frequency the same no mater the drag force?, since it is outside the cos and sin part of the equation?
By convention, we use angles up to 10 degrees for our small angle approximation, but 60 degrees is far beyond the acceptable limit. Did you misspeak and say 60 degrees when you meant 6 degrees?
Consider that the pendulum is at rest with θ_0>0, measured counterclockwise. When the motion starts, pendulum acquires angular velocity dθ/dt in the clockwise sense. So dθ/dt0, we have:
F_gravitational = -g/L*θ
F_resistance= -γ*dθ/dt
you assume it but it's wrong
you just modeled a simple damper . air resistance isn't that.
For sure, you're right!
One could model the aerodynamic drag with a force with magnitude equal to Cd*ρ*V²*A/2, where Cd is the drag coefficient (that may also vary with the Reynolds number of the flow). That would produce an non linear ODE that is hard to be analytically solved, as presented below.
d2θ/dt2 + γ*(dθ/dt)² + g/L*θ = 0
Of course it is possible to solve this equation numerically, but the reason to model the drag force as a linear function of the speed is only to simplify the calculations, once the ODE obtained is linear and can be easliy solved:
d2θ/dt2 + γ*dθ/dt + g/L*θ = 0
Great video. One question, how do you go about finding gamma and is the density of the medium the only factor in finding it or does it also involve other things like the incident area of the mass?
And would you actually calculate gamma for the value of air resistence?! Could please make a video deepening a little bit more about the matter...?! Please!!!
This is quite interesting!!!
7:46
I have seen that memed
Many many many many many times
Can you suggest some resources to self study physics in the next video?(mathematical methods and all)
Very convincing video...still we didn't get to terminal velocity of the pendulum ...lol
Amazing video , keep explaining love this content
Can you pls explain or make video on time period of a vertical circular motion for a Bob attached to a string.(for minimum condition which is at top the speed of Bob is square root of rg where r is radius and g acceleration due to gravity) I am not even able to get the formula anywhere on the net or books forget about the derivation. Pls help
*Huge fan from India*
I love physics and I like it video
Minor constructive comment: maybe you could have mentioned that the small angle approximation only works if the angle is given in radians. As you were talking about the approximation being valid up to 60 degrees some confusion may have been caused.
Is the final equation we acquire applicable to the simple harmonic pendulum as well, considering that the angle doesn't exceed 20 degrees in SP
Hello..very well your video.. I want to know about space time relativity. I hope you Will give more videos about Space time and time dilation
Top qaulity video as always parth
My first time seeing the equation for the motion of pendulum that takes air resistance into account
What is A and B in the modified equation???
how do i know how the proportionality constant changes which the surface area of the bob increases
why dont you start online courses?
Thank you for the amazing videos.
Please make videos about rotational dynamics
isnt Fd = 0.5ρAcV^2 which is 0.5ρAcL^2(dθ/dt)^2
You are correct. I referred to this in my comment also, his assumption regarding drag force being proportional to velocity is incorrect.
he used a simple damper as if it a drag force.
so of course the final result would seem correct.
Not necessarily. Drag force can act both proportional to v and v^2 depending on whether it is laminar or turbulent in nature. The drag equation you mentioned assumes that an object is moving at a high enough velocity to have a high enough reynolds number to assume turbulent flow. This isn't necessarily the case with the pendulum.
I have a better understanding of drag force now. After watching the video.
Hey Parth I would appreciate if u did a video about light dispersion at minimum deviation in prism
I am just amazed how we managed to describe nature by just 1 differential equation
Can't the air drag be made regenerative to some extent so that the pendulum oscillates a little longer.
For sure. The 6 dof equations become much simpler once your vehicle reaches the vacuum of space. Air resistance is very important.
But does air resistance depends on the composition if the air and the number of molecules?
8:20 The solution to a second order differential (it has a second derivative) like this, is a function with a second derivative equal to the negative of the original function. Sine is a solution because the derivative of sine is cosine, and the derivative of cosine is negative sine. We can also write the sine as a function of exponentials and find an exponential solution, but that is too difficult for this video.
paul dirac equation next please ??
make sense but how more far we can push that padular effect.. i'm stuck on that theory since 2005 involving money... & energy & connaissance. because my boss stole my idea. and integrated in is business process.. and there internal security service have a part of is system on the same taxe credits that is buit the structural of it... can you develop ??????
If the speed of the object is infinite, is drag is also infinite?
2:10 if the two forces cancel eachother out, then why would the object still fall and not just float in the air at its current position?
it would stop and float only if the drag force was equal to the weight of the object the moment it has 0 velocity. But when it is equalized at a certain time when it has (u) downward velocity there will be no net force to decelerate it (ΣF=ma=0)
I am 14 and i'm practicing with a program in my country for the physics olympiad
Air resistance matter!
Aviation Engineer : You guys ignored air resistance?
Please make a discord server where we can discuss . I have been writing this in ur many vid still u are not replying. But u are the best
"Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass. With air resistance acting on an object that has been dropped, the object will eventually reach a terminal velocity, which is around 53 m/s (190 km/h or 118 mph) for a human skydiver."
Now I'm gonna pretend that I didn't see it ! 😅
The heck are u doin here
Not ignoring air resistance is one of the great reason for Spherical Cow Syndrome.
triggered engineer here. did you just use the small angle approximation for angles up to 60 degrees? we get shit from the mathematicians and physicists for using it up to 5 degrees in some circumstances. that's ridiculous.