Multi degree of freedom - determining equation of motion

A picture of the system has been attached. There is no friction between m and m1. How would you determine the coordinates to describe the system and the equations of motion?

1) For the two degree of freedom structure shown:
i) what is the matrix equation of motion?. Assume that m1 and m2 oscillate harmonically with the same frequency but with different amplitudes X1 and X2 of x1(t) and x2(t).
ii) what are the values of the amplitude ratios r1 and r2
if m1 = m2 = m, k1 = k, and k2 =3k?
See a

For this two degree fo freedom model, how do I find the matrix equation of motion?
How do I find the value of the modal ratios if m1=m2=m, k1=k and k2=3k?
If a force of 25sin3t is applied to m2, how do I find the value of the response if m1=m2=1 slug, k1=10lb/ft and k2=30lb/ft?

Sample of question (Please refer to attached PDF document for full details):
We have at our disposal an amount of energy equaling 3.5kJ and we wish to allocate 1 mole of gas which occupies volume V.

A bead of mass m moves on a parabolic wire with equation z=(1/2*x^2), where z measures the height of the bead and x is the horizontal distance in the plane of the wire. The plane in which the wire lies rotates about a fixed vertical axis passing through x = 0, so that its angle relative to a fixed plane is ΓΈ. (See attachment fo

Question: A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x=5(pi/t +pi/3). The velocity (in m/s) of the body at t=1 second is equal to what value?

The following regression equation was computed from a sample of 20 observations:
Y' = 15 - 5X
SSE was found to be 100 and SS total 400.
a) Determine the standard error of estimate.
b) Determine the coefficient of determination.
c) Determine the coefficient of correlation.

An object executing simple harmonic motion has a maximum speed of 4.3 m/s and a maximum acceleration of 0.65 m/s^2.
Find (a) the amplitude and (b) the period of this motion.