Calculating Oscillation Period and Spring Energy in a Three-Mass System

[lenna_kay]

Homework Statement

In the equilibrium of the system shown in the diagram, the spring is stretched by 7cm compared to its undeformed state. The masses are:
M1=300g
M2=100g
M3=100g

Calculate the period of oscillation of this system if the weight is pulled downward and released, as well as the energy of the spring.

Relevant Equations

It's a junior year AP problem about oscilations and harmonic oscilators. So T=2pi/w formula and everything in the same bracket

To be frank im not exactly sure where to even start. We were given a diagram in which two masses (m1 and m2) are connected by string which is draped over a circle (m3) that is fixed on the ceiling. From m2 is hanging a spring which is, i guess, attached to the floor. The question asks what would happen if we pulled m1 from the equilibrium it is in and let it fall.

If anyone has any idea on how to solve this i would really appreciate it. Also, if there are any follow up questions id be happy to elaborate. My description might not be the best since english is my second language and I haven't yet found out the way to attach pictures on the forum.

All the best

 

[berkeman]

Welcome to PF.

I haven't yet found out the way to attach pictures on the forum.

Use the "Attach files" link below the Edit window to upload your file.

 

[lenna_kay]

Welcome to PF.


Use the "Attach files" link below the Edit window to upload your file.

Thank you for the instruction! Ive added the image

 

[berkeman]

To be frank im not exactly sure where to even start.

Are you able to solve a simpler problem first? Say, a single mass hanging by a spring from the ceiling, and you release it from a position where the spring is relaxed (so not exerting any force on the mass)... How would you calculate the motion of the mass versus time in that simplified situation, and what would the frequency of oscillation of that system be?

 

[haruspex]

It is often possible to "straighten out" pulley systems where masses move in synchrony. In regard to inertia the masses add, while in regard to gravitation they oppose.
Also, in equilibrium, the spring force exactly cancels the net gravitational force.

If $m-1$ is pulled down a distance x, what is the net restoring force?
What acceleration will that result in?