Please answer both! I have an idea of how to do the first one, but I've only worked the version where the k are equal for both springs and the equation if motion looks simpler. I'm worried I'm on the wrong track?

1. Two masses, ma=1kg and my = 2kg are connected by two different springs with spring constants , = 3//m and As = 2NV/m as in the Figure. Suppose at t = 0, m, is displaced a distance .'a = lem from Pa and ma is displaced a distance co - 2cm from A and both masses are released from rest. Assume no friction or external forces. a) (10 points) Find the equations of motion, Fa(t) and as(t) b) (20 points) Find the eigenvalues, also called the normal mode frequencies* c) (10 points) Identify the solution of these equations given the initial conditions. 2. Figure 2 depicts three masses, my, ma, and my connected by springs. The springs on cither end are connected to walls. YOU MAY ASSUME ki = ke - ks = ka and that all the masses are the same. a) (20 points) Find the equations of motion for this system. b) (30 points) Find the normal mode frequencies, w for this system. c) (10 points) Can you identify what motion the three eigenvectors identify in the system? ka PROBLEM 1 PROBLEMZ