Electric Circuit Analogy for Spring-Mass-Damper Mechanical System

What is the Electric Circuit Analogy for Mechanical System involving Force, Mass, Damper and Spring? How can we model Mass-spring-damper mechanical system using electric circuit elements including resistor, capacitor, inductor and even operational amplifiers? These questions are discussed in this tutorial video that highlights three methods for Mass-spring-damper modeling using electric circuits. The first method is referred to as force-voltage method, models the force as a voltage source, displacement as electric charge and hence derivative of displacement as the electric current, mass as inductor, damper as resistor with resistance equal to the damping coefficient (b), and spring as capacitor with capacitance equal to the inverse spring constant (1/k). Newton's second law of motion is represented with Kirchhoff's KVL circuit voltage Law. The second method is referred to as force-current method that models applied mechanical force as the electric current source at the input of the electric circuit. The derivative of displacement is modeled as the voltage, mass as capacitor, damper as resistor with resistance equal to the inverse of damping coefficient (1/b) meaning damping coefficient serves as electric conductance, and spring as inductor with inductance equal to the inverse spring constant (1/k). Newton's second law of motion is represented with Kirchhoff's KCL circuit current Law. The third presented circuit equivalent of mechanical system introduces a new electric circuit elements whose voltage is proportional to the second derivative of its current. This new circuit element effectively computes the second derivative of current and reports it as the voltage across its two terminals. It is implemented using two Op Amps, two capacitors and a few resistors. To see more analysis about this new circuit elements please see my follow-up UA-cam video "Impedance Converter Analog Circuit Design with Op Amp" • Impedance Converter An... . In the third method, mechanical force is modeled as a voltage source, the displacement is modeled as the current, spring as resistor with resistance equal to the spring proportionality constant (k), damper as inductor with inductance equal to damping coefficient (b), and mass as the new circuit element that has a voltage proportional to the second derivative of its current. Newton's second law of motion is represented with Kirchhoff's KVL circuit voltage Law.

[@jeanaimarre8605]

You are one of the best lecturer I have ever heard. Thank you, your video are a treasure.

[@STEMprof]

You're very welcome. Thank you. Glad that you like my channel. For more examples please see:
Double spring-mass mechanical system analysis using Laplace Transform ua-cam.com/video/I5qTyPIo-xg/v-deo.html
PID Controller for Servo Motor explained ua-cam.com/video/NATBlfABXrA/v-deo.html
Thermocouple Amplifier with Cold Junction Compensation Explained ua-cam.com/video/-BsDLBI166U/v-deo.html
Laplace Transform to solve spring mass mechanical system ua-cam.com/video/I4mqQQ9hSKc/v-deo.html
I hope these videos are interesting as well.

[@miszcz310]

Very interesting video, thank you.

[@STEMprof]

You are welcome. Thank you. Glad that you liked this video. For more examples please see:
PID Controller for Servo Motor explained ua-cam.com/video/NATBlfABXrA/v-deo.html
using Laplace Transform to solve spring mass mechanical system ua-cam.com/video/I4mqQQ9hSKc/v-deo.html
Double spring-mass mechanical system analysis using Laplace Transform ua-cam.com/video/I5qTyPIo-xg/v-deo.html

[@STEMprof]

What is the Electric Circuit Analogy for Mechanical System involving Force, Mass, Damper and Spring? How can we model Mass-spring-damper mechanical system using electric circuit elements including resistor, capacitor, inductor and even operational amplifiers? These questions are discussed in this tutorial video that highlights three methods for Mass-spring-damper modeling using electric circuits. To learn more about the op amp based circuit element discussed in this video please see my UA-cam video "Impedance Converter Analog Circuit Design with Op Amp" ua-cam.com/video/o6l_wztCACQ/v-deo.html .
And for more example see the following two UA-cam playlist in my channel: Modeling mechanical systems ua-cam.com/play/PLrwXF7N522y7yLh4HCtAahCZ-Sq88OXhW.html
Analog and Digital Circuit Design Videos ua-cam.com/play/PLrwXF7N522y4c7c-8KBjrwd7IyaZfWxyt.html