Coupled Oscillation attached at one end ?

[GodPlaysDice]

Homework Statement

I'm supposed to determine the equation of motion of the two masses on the worksheet. I just need to start with that. Here is the problem statement:
http://www.physics.udel.edu/~jim/PHYS211_14S/Homework%20assignments/Assignment%205%20-%20coupled%20oscillations.pdf

Homework Equations

I'm assuming x = Acos(ωt) has something to do with it as well as the energy of a spring-mass system
K + U.

The Attempt at a Solution

I don't know where to start. This is where I need the helping. Thank you for anyone who helps.

 

[paisiello2]

It's very astute of you guessing the form of x. That is key to determining the solution of the differential equation. However, if the question is only asking for the equations of motion then I would interpret this to mean you don't have to solve the differential equation for x.

And although you could solve the problem using energy methods it is not usually the convention since this involves extra work that really isn't necessary I think in this case.