Mass Spring Dampers: Equation of Motion | Dampened Harmonic Motion

Look at how a damper or dashpot contributes to the damped oscillation of a mass on a spring. By deriving the equation of motion from Newton's second law we can see how an external force such as gravity, the elastic or spring force and spring constant along with a damping coefficient contribute individually to dampened harmonic motion.

Once the equation of motion is derived, note the equation is a second order linear differential equation that can be solved using a Laplace Transform then rearranged for a transfer function.

Then we will plug in the equation of motion into a simple graphing program in order to visualize the oscillatory motion of a mass spring damping system. See the only difference between simple harmonic motion and dampened harmonic motion is the addition of a damper.

This problem typically comes up in college physics as well as differential equation courses. In practical application this problem comes up in everything from vehicle suspension theory all the way to the motion of individual particles in certain systems.

[adalbertolima]

I graduated in mechanical engineering 2 years ago, you don't use everything you learned everyday and eventually you start to slowly forget what you learned. Thank you for the refresher, I think videos like this do so much more because you explain how the variables affect the system, something that wasn't always made fully clear to use during college.

[aka]

i just cant tell you how smooth that was !! thanks brother

[ceciliamartindale]

A friend just sent this over - super helpful!

[datphan]

This movie is so interesting. I hope you will have more good videos in the future.

[Strummustunes]

insanely clear explanation, thanks for your great work

[aswajiths]

Nice bro excellent work. Bro can you please similar videos for different concepts in physics?

[trentvlak]

Oh, mountain forks have damping? I guess we're not talking about Rockshox motion control haha.

[KelechiNgwu-gq]

How does one go about evaluating one of the variables, say b

[dilarayilmaz]

Video is very helpful for me. Please tell me, which program did you use for plot of motion ?

[laurentmuller]

Any way you could create a model including spring preload (as available on an MC shock) as a variable? The internet is full of righteous explainers blasting that preload is not affecting stiffness (sure, it has no effect on k)...but fail to explain why the suspension "feels" stiffer with more preload. Thank you for the great video.

[samo]

hello I loved this video so much, but I want to know how to make this excel sheet form this equation

[kutluhankahraman]

Hi! could you explain how did plot the motion in excel? I would like to try it by myself

[razistmt]

Nice, good explanation. thanks so much

[felipequinones]

Where i can find the excel for the damping?

[Toxic__rl]

x_ddot = d^2 x / dt^2... but besides that awesome vid