Max Amplitude for a 2 mass oscillation system

AI Thread Summary
The discussion focuses on determining the maximum amplitude for a two-mass oscillation system to maintain simple harmonic motion. As amplitude increases, the acceleration of the masses also increases, potentially leading to slack in the connecting string when acceleration exceeds gravitational force. The relationship between maximum acceleration and amplitude is expressed with the formula acc max = A w^2. Additionally, the condition for maximum amplitude is derived as A = 2gm/k, where "g" is gravitational acceleration, "m" is mass, and "k" is the spring constant. Understanding these dynamics is crucial for analyzing the behavior of the oscillation system.
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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" ?
 
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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?
 
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.
 
acc max = A w^2

g = A K/2m

A= 2gm/k
 

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