Spring Mass Damper equilibrium

eddie_spaghetti

Hi there, thanks for taking the time to read my post, any help would be appreciated.

I am analysing a 2 D.O.F. spring-mass-damper system, which is laid out in the following way (apologies for the lack of a proper diagram, my scanner is dead):


wall---spring1----mass1----spring2-----mass2----spring3----wall
wall---damper1---mass1----damper2----mass2----damper3--wall
| |
|--->x1 |--->x2


There are 2 time dependent forces (F1 and F2) acting on the masses and the coordinates x1 and x2 are chosen such that the springs exert zero forces when x1 and x2 are equal to zero.

I have drawn the free body diagrams for each mass, and written the equations of motion for each as;


I missed out a couple of details but I hope my maths is correct there.

I have then been asked to find the equilibrium points( ie. the points at which xdot and xdoubledot=0.) of the system when the input forces F1 and F2 are 0. There is clearly one at x1 and x2 = 0.

Am I wrong in thinking that 0,0 is the only equilibrium point?

[edit]Think I've got it...I think I should be looking for the other equilibrium points as functions of the spring constants.[/edit]
Thanks,
Ed