Period of oscillation of spring system

AI Thread Summary
The discussion focuses on determining the period of oscillation for a spring system consisting of two blocks, each of mass M, connected by a spring with force constant k. When the left block is released from a compressed position against a wall, the period of oscillation is given as period = 2(pi)sqrt(M/(2k)), which arises from considering the reduced mass of the system as M/2. Participants express confusion about the motion of the right block after the left block leaves the wall and seek clarification on the mechanics involved. Visualizing the motion and understanding the effective spring constant, which doubles when considering the spring's two halves, is emphasized as crucial for grasping the problem. The discussion highlights the need for further explanation and possibly visual aids to clarify the dynamics of the system.
SbCl3
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1. Question
A system consists of two blocks, each of mass M, connected by a spring of force constant k. The system is initially shoved against a wall so that the spring is compressed a distance D from its original uncompressed length. The floor is frictionless. The system is now released with no initial velocity. (See picture)

[part c] Determine the period of oscillation for the system when the left-hand block is no longer in contact with the wall.

Homework Equations



period = 2(pi)sqrt(m/k)

The Attempt at a Solution



The answer given is this: period = 2(pi)sqrt(M/(2k))
The explanation given is "m = reduced mass = M/2".

I don't understand the explanation given. I can't visualize what happens to the right mass M after the left mass M leaves the wall. This is different from all spring problems I have seen, where one end is attached to a wall, so of course I suspect a different answer. Could someone show me the math involved to prove the period is reduced like this?
 

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SbCl3 said:
The answer given is this: period = 2(pi)sqrt(M/(2k))
The explanation given is "m = reduced mass = M/2".

I don't understand the explanation given. I can't visualize what happens to the right mass M after the left mass M leaves the wall. This is different from all spring problems I have seen, where one end is attached to a wall, so of course I suspect a different answer. Could someone show me the math involved to prove the period is reduced like this?

Hi SbCl3! :smile:

Divide the spring into two halves, then you can consider each half to be fixed against a wall (in c.o.m. frame of reference, of course) … the spring constant is doubled (1/K = 1/k + 1/k), and the mass is M :wink:
 
Can anyone please describe the motion qualitatively? I cannot visualize this problem. After the blow, the spring is maximally compressed and the block on the right moves to the right, away from the wall. I know that the left mass leaves the wall the first time that the right mass has its maximum speed to the right and the spring is at its equilibrium length. But I have no idea how the motion is after that.

All help appreciated.
Thanks
 
Please help this question has been giving me nightmares.
 
does anyone have a link to an animation
 
guys?
 

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