A mass (M) is connected to two oscillating supports with springs (mass in the middle, then single spring on each side connecting to a moving support). The left support oscillates at $\displaystyle X_1=Acos(wt)$ and the right hand support oscillates at $\displaystyle L_0+Bwsin(wt)$ where $\displaystyle w$ is the angular frequency, and $\displaystyle L_0$ is the separation between the supports when the system is at rest.

If $\displaystyle X(t)$ is the position of the mass relative to the origin, find a ODE for $\displaystyle X(t)$ and find the location of the mass when at equillibrium/rest. That is, find the position of the mass when its velocity and acceleration are both 0, assuming that A=0 and B=0. Both springs satisfy Hooke's law with constants of $\displaystyle k_1 and k_2$

Thats the problem statement.

I know that this has to be a second order ODE because it's oscillating. Also, I know the form of a mass on the end of a single spring is $\displaystyle mx''(t)+kx(t)=0$ but I have no idea when it's placed in between.

How do I start? Just a little nudge in the right direction please.