Four mass-spring-damper system State Space Model

[EricHong]

Please, help. The question is stated inside the file.

Thanks in advance,

Eric

[AlanStevens · Accepted solution]

You're asking Mathcad to find an analytical solution to an 8'th order polynomial! Can't be done above 4th order! Stick with numerical solutions.

Alan

[wayne]

Eric

The last equation has kc, but should be kd

Mathcad has functions for eigenvalues (eignevals) and it will provide numerical results ( I tried it on your corrected matrix), but not symbolic, as Alan indicates
Even if you could get one, it would probably be so long as to be unuseable.

[EricHong]

Thanks. It's kc alright. There's no kd. kc is the spring between mc and md.

After all, Alan is right.

Thank you all,

Eric

[wayne]

You have 4 masses connected with 3 springs? After lookiing at the matrix again, it's not clear to me what the arrangement would be? Just for my own curisoty, could you pass along?

Thanks

Wayne

[EricHong]

see the attached.

note that the system is not ground at any point. the dampers are shown to ground, but you can think of them as sliding masses on a viscous surface. due to a unique nature of the system, damping isn't a funciton of delta velocity between masses.

thanks,

eric

[wayne]

Eric,
Interesting problem, thanks for the reply.

Wayne