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 and the right hand support oscillates at where is the angular frequency, and is the separation between the supports when the system is at rest.
If is the position of the mass relative to the origin, find a ODE for 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
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 but I have no idea when it's placed in between.
How do I start? Just a little nudge in the right direction please.