Spring Mass Damper Model (suspension system)

Modeling of systems is essential when designing a control system. We treat the modeling of systems through examples, in this video we model the dynamics of a vehicle suspension system. Using the idealized components of a spring, mass, and damper the governing equation of motion is derived.
** Follow us on Instagram for more endless engineering:
/ endlesseng
** Like us on Facebook:
/ endlesseng
** Check us out on twitter:
/ endlesseng
** First image for suspension is courtesy of PXhere and is in CC0 Public Domain
** The leaf suspension image is courtesy of Tennen-Gas from WikiMedia commons, these images are licensed under GNU Free Documentation License.

[@bbatuhankayaa]

This was helpful to get the logic of a spring-mass damper system in a suspension system. I need this one for my coursework. Thanks!

[@EndlessEngineering]

I am glad this was helpful Batuhan! Please let me know what other content you would like to see

[@brenn7754]

How do we account for the force of gravity on the system?

[@EndlessEngineering]

Hi BreN, typically with a spring mass damper system the gravity term can be neglected as it would not affect the dynamic motion of the system. Gravity would only affect the resting position of the spring after the mass is hung. You can find a proof for this in any mechanical vibrations text book

[@6glob]

7:21 Why don't we add weight (mg) as a force in the Newton's second law formula or the Free Body Diagram?

[@EndlessEngineering]

Gravity only shifts the equilibrium point of the spring-mass-damper, at rest a vertical spring will deform due to gravity. But gravity does not affect the dynamics of the system

[@inthebackwiththerabbish]

I need this for mathematics. Thank you very much

[@EndlessEngineering]

Thank you for watching, glad you found it useful

[@dhairyashah9275]

Can we write a transfer function for the above system? If so could you explain how? Thank you.

[@EndlessEngineering]

Hi Dhairya, please checkout my video on Accelerometer Modeling (link below) it has an example of a pring-mass-damper TF kzbin.info/www/bejne/kJDOg3hnf897g9U

[@wessamabousada7251]

and if we assume that the vehicle is not moving so Fr must be 0 , which means the system is nonlinear , i hope to get the answer asap, i'd really appreciate it

[@awaisahmed5471]

The system is still linear regardless of whether there is a forcing function or not. If Fr is 0, the system is still linear however it will also be homogenous

[@wessamabousada7251]

Fr must be given ,is that right ?

[@Trevdog2392]

why isn't force of gravity included in the FBD?

[@EndlessEngineering]

Great question! When all the elements follow linear constitutive laws (i.e., spring, F=kx, damper, F=cV), the effect of gravity will not influence the dynamics. Only the equilibrium position (at rest) of the mass will be changed by gravity. There are mathematical proofs that show that.

[@Final1Boss]

@@EndlessEngineering new information! thank you!

[@BETAG0]

What kind of markers are u using? Those are dope

[@EndlessEngineering]

I use Expo Neon markers, they work their magic!

[@BETAG0]

Im a student from South Korea! Your video was very helpful. Thank you so much

[@EndlessEngineering]

@@BETAG0 I am glad you found the video helpful! Thank you for watching