Equations of Motion and MATLAB/Python Simulation of Multibody Spring-Mass-Damper System

In this video we take a look at a two-cart spring-mass-damper system. The equations of motion for the 2 DOF system are derived using simple Newtonian mechanics and solved numerically in both Python and MATLAB. The results are analyzed and a MATLAB animation is presented to visualize the results.

Equations of Motion Derivation:

Python Code:

MATLAB Code:

[thrashingmetal]

Beautiful work, continue, more examples like these with simscape

[ThaChikenMan]

Hi there, I have a project where it is a similar example to the one you showed, but instead there is a force component that is not negligible for the first 50 seconds of a 300 second time span. After the first 50 seconds, the force turns into zero. I tried incorporating that into the acceleration equations, but when I graph it, it ends up being an exponential graph for position and it just becomes a flat line as it peaks in value. Any input? Thanks a lot.

[henrymosgeralulus]

Nice video, thank you.
But, pay attention to the equation X1(double dot) = 1/m1 * ( - b1 * x1 + minute 3:23. Will you consider as - b1 * x1 (dot) ?

[glennc.vidalurquiza]

Thanks by sharing this information. This is direct to the subject. The materials that your provided is very useful. Thanks again.

[AA-hrul]

you are great very much thnx but i get this error? how can i get rid of that? btw line

[ll-trhh]

you're a blessing, man. thanks for sharing.

[shanmukharao]

Dear Ironpine this video is really helpful Thanku man

[leemontgomery]

Really informative video. I am only a lower level novice Matlab user so I am still learning the basics. I want to get to this level, someday.

Thanks again.

[huthali]

Thanks a lot for the explanation, if I have a bar how can give it an angle at matlab

[cleberfeitosa]

Great video! I'm just having a problem with the animation, I'm pretty sure my computer could handle it smooth, bud it gets incredibly slow. Is there anything I can adjust to make smoother?

[hc]

Hello sir, you made a great explanation. thank you.

[josh]

Hi, currently working on a similar problem of my own and found this video very helpful. However in my problem i don't think I can assume f(t) to be zero as it is a unit step input. Would you know how to change the code for this? struggling to find anything else on this topic online. Thanks!

[AJ-etvf]

Hey man! Thank you so much for this! This is awesome. I'm familiar with Python and MATLAB and have used both (and also Julia!) to solve vibration problems. What I'm not very knowledgeable of though is the required animation knowledge to animate spring-mass systems like these. How did you learn to animate these? What/where are the resources that I can use to learn these myself? This also because I am interested in animating a 3-degree-of-freedom spring-mass system. I'm sure I can study and learn from your code but I'd appreciate to know and learn what resources I can study to make animations myself so I'm not just copy-pasting code.

That's all, thank you very much. Your work is highly appreciated and I wish it has more views. I'm very glad to have found this in Youtube.

[classicalguitararchive]

how can i make system fixed both end and have 3 spring?

[cevheryusufinan]

Thanks for such an informative video. May I use the codes for my capstone project? Is there any copy-rights policy?

[Urja_PGDBA]

what if I only want one mass spring system where it is attached to wall on one side and a force is applied on the other side

[amritaryal]

Hello sir, i need to solve for 'n ' number of spring and mass system. How can i modify this code. I need solid hint. Thank you

[chandrasekhar]

Thank u fr ur nice explanation sir can u tell how to apply a control force while trying to control structure responses by active control

[yogendrasinghchauhan]

How u done the animation thing (Nice Vdo) PLEASE MAKE A DETAILED VDO

[alfonsormichel]

Hi. Really great video, and very helpful. But there is something that does'nt make sense for me: if I apply a force in "m2" to the right side: why "m1" body starts its movement to the left side?

Thank you in advance