Two masses, M and 4M, are on opposite ends of a massless spring, sitting on a frictionless, horizontal table. The spring is compressed, and the spring-and-masses system is released from rest. If mass M oscillates with amplitude A and frequency f, then mass 4M will oscillate with ?
list of choices are attached
ω2M=k, center of mass, xmax=A
The Attempt at a Solution
for mass 1 : ω2M=k, (2∏f)2M=k
center of mass 1: MA/M+4M = A/5
for mass 2: ω24M=k, (2∏f)24M=k, 4∏(f/2)24M=k
center of mass 2: 4MnA/M+4M = 4nA/5
-since both masses are on the same spring they have the same spring constant so for each of the masses it should be equal but for 4M the frequency had to be f/2 in order for it to be squared and cancel the 4 in 4M, however I'm not sure.
I used the set the equilibrium point as the reference point for center of mass, but got kind of confused.