Max Amplitude for a 2 mass oscillation system

[daredevile125]

Homework Statement

A mass of "m" is attached to the bottom of a vertical suspended spring with spring constant "k". Attached to that mass is a string , that is connected to a second mass also equal to "m".

What is the maximum amplitude for the two-mass oscillation system in order for it to remain "simple harmonic" ?

 

[Spinnor]

As the amplitude increases the acceleration of the masses increases. When the acceleration is greater then that of gravity there will be slack in the string?

 

[daredevile125]

ahh thank you that sounds reasonable, I was thinking it had something to do with the spring being inelastic anymore , but that makes more sense , tyvm.

 

[daredevile125]

acc max = A w^2

g = A K/2m

A= 2gm/k