It is completely pleasant to solve the differential equations, plot the graph and watch your result in a real thing! Thank you! It made the things easier to grasp
The third mode is a really good example of a nontrivial solution, for diff eq motivation. The mode makes sense, but you can’t confirm it until you see it in math or empirically. Very nice
There seems to be an exponential decay to the oscillation of one of the masses in the coupled motion whilst it trades the amplitude of motion and energy. Could this behaviour be described mathematically as an exponentially damped sinusoidal wave that recomposes itself after an ever-decaying amount of cycles? .
the "decay" is not exponential . . . instead, the amplitude of each pendulum's oscillation is a cosine function, with the two pendulum cosine functions being 90 degree out of phase. The amplitude of one of the pendulums looks like xA(t) = Xo Cos( (w1+w2)*t/2)*Cos( (w1-w2)*t/2), where w1 and w2 are the two natural frequencies of the 2-dof system. The motion is a combination of the average frequency (the swinging oscillation) and the difference frequency (the slower exchange of energy). Here is an animation of the coupled motion, with a graph of what each mass is doing as a function of time: www.acs.psu.edu/drussell/Demos/coupled/coupled.html
well -- he is kind of right, but not completely. The coupled motion is NOT a superposition of the two natural modes of the system. Instead, it is the result of a special, specific initial condition situation where both masses are initially at rest with one mass at its equilibrium and the other mass displaced away from equilibrium.
Hello, I'm using parts of this video in making my video about coupled oscillator. I am a student of BUET. I have made a Javascript based animation that mimics this spring coupled pendulum. I hope you are okay with that.
If both masses were released from their equilibrium positions, nothing would happen at all. In the equilibrium condition, the net force on the system is zero, and there would be no acceleration, and the system would remain at rest with no oscillation. At least one of the masses must have an initial displacement from equilibrium in order for oscillation to occur. The special "coupling" case shown in this demonstration occurs when one mass is initially displaced from equilibrium while the other is at rest at equilibrium.
I was thinking if it would be possible to carry out an experiment showing an amazing result predicted by the SEA : Statistical Energy Analysis. If the excitation is random on both pendulum then we sould observe irreversibility of energy. ..
![[DEMONSTRATION] - Coupled Oscillators](http://i.ytimg.com/vi/ljaQr6YOVnk/mqdefault.jpg)
![[DEMONSTRATION] - Coupled Oscillators](/img/tr.png)
The lack of bagpipe music really helps
Great video! You know what it's missing though? Some epic bagpipe background music
thanks! that actually made me laugh . . . if only there was a version somewhere with some epic jazz bagpiper playing "swing low, sweet chariot"!
It is completely pleasant to solve the differential equations, plot the graph and watch your result in a real thing!
Thank you! It made the things easier to grasp
Best video on UA-cam for coupled oscillators😊😁
The third mode is a really good example of a nontrivial solution, for diff eq motivation. The mode makes sense, but you can’t confirm it until you see it in math or empirically. Very nice
Thanks for adding this noiseless version of video.
Needed this for my Game Physics course. Thanks!
I haven't seen the original but can someone edit the bagpipes back in, I think it could help
Sir can you show two double pendulums released from similar angle and in similar state. Thay how it goes chaotic
There seems to be an exponential decay to the oscillation of one of the masses in the coupled motion whilst it trades the amplitude of motion and energy. Could this behaviour be described mathematically as an exponentially damped sinusoidal wave that recomposes itself after an ever-decaying amount of cycles? .
the "decay" is not exponential . . . instead, the amplitude of each pendulum's oscillation is a cosine function, with the two pendulum cosine functions being 90 degree out of phase. The amplitude of one of the pendulums looks like xA(t) = Xo Cos( (w1+w2)*t/2)*Cos( (w1-w2)*t/2), where w1 and w2 are the two natural frequencies of the 2-dof system. The motion is a combination of the average frequency (the swinging oscillation) and the difference frequency (the slower exchange of energy). Here is an animation of the coupled motion, with a graph of what each mass is doing as a function of time: www.acs.psu.edu/drussell/Demos/coupled/coupled.html
ma shaa Allah..thank you
Disliking bagpipe music? How is it possible... By the way rnnnmt, it's bagpipe music, not "noise"
Verifying if MinutePhysics was correct. Damn was he right.
well -- he is kind of right, but not completely. The coupled motion is NOT a superposition of the two natural modes of the system. Instead, it is the result of a special, specific initial condition situation where both masses are initially at rest with one mass at its equilibrium and the other mass displaced away from equilibrium.
m from india n u explain s very well
Hello, I'm using parts of this video in making my video about coupled oscillator.
I am a student of BUET.
I have made a Javascript based animation that mimics this spring coupled pendulum.
I hope you are okay with that.
Can you provide us the source code or a demo for your program?
Thanks and how could I use that in a simple audio project?
Whats the difference between it being released from a displaced position and from an equilibrium position?
If both masses were released from their equilibrium positions, nothing would happen at all. In the equilibrium condition, the net force on the system is zero, and there would be no acceleration, and the system would remain at rest with no oscillation. At least one of the masses must have an initial displacement from equilibrium in order for oscillation to occur. The special "coupling" case shown in this demonstration occurs when one mass is initially displaced from equilibrium while the other is at rest at equilibrium.
@@DanRussellPSU Thank you so much! I'm doing this for my physics project and that helped a lot.
I was thinking if it would be possible to carry out an experiment showing an amazing result predicted by the SEA : Statistical Energy Analysis. If the excitation is random on both pendulum then we sould observe irreversibility of energy. ..
What is the lenght and the constant k of the springs?
I need the bagpipe inside me
If the calculation here being will be perfect
@minutephysics
Where is the bagpipe version?
It's on my UA-cam Channel . . . ua-cam.com/video/YyOUJUOUvso/v-deo.html
😍😍😍😍
I prefer noise to bagpipe music
Muito legal!
🔜
Cute😍🥰😘⁉️
Sorry😣