Damped mass spring system with with external forcing function

[kstylian]

Hi All,

This is my first post here, and thanks in advance for any help and direction.

I'm trying to model an enclosed damped mass spring system with an external forcing function acting on the system (not on the mass directly). Ultimately I would like to plot/calculate the motion (y) of the mass relative to the system, supposing the forcing function is sinusoidal.

Please see attachment.

Thanks again.

 

[kstylian]

Is this really as simple as: ??

 

[Curl]

yes, now find the homogeneous solution (easy) and the particular solution (guess Acos(wt)+Bsin(wt) and solve for A and B) and add those up.

You can also do this by finding the system's transfer function, but in this case its not worth bothering yourself with that:
http://en.wikipedia.org/wiki/Transfer_function

 

[kstylian]

Thanks. I'll try that...

The reason I posted is that I'm interested in steady state motion of the mass displacement relative to the system ONLY...not system + forcing function amplitude.

Will the homogeneous + particular solution provide this, or is there more to it...?

Thanks again!

 

[PJC01]

Hello and welcome to the forum!

It sounds like you are working on a very interesting problem. The damped mass spring system with external forcing function is a common model used in many fields of science and engineering, including mechanical, electrical, and chemical systems.

To simulate and analyze this system, you will need to use a combination of mathematical modeling and numerical methods. You will first need to set up the equations of motion for the system, taking into account the external forcing function and the damping factor. These equations can then be solved using numerical methods such as Euler's method or Runge-Kutta methods.

Once you have the solutions for the equations of motion, you can then plot the motion of the mass over time. As you mentioned, if the forcing function is sinusoidal, the motion of the mass will also be sinusoidal but with a different amplitude and phase shift. You can use tools such as MATLAB or Python to plot and analyze the results.

I hope this helps get you started on your project. Good luck!