# Period of oscillation of spring system

1. Mar 30, 2009

### SbCl3

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.

2. Relevant equations

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

3. 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?

#### Attached Files:

• ###### temp.png
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2. Mar 31, 2009

### tiny-tim

Hi SbCl3!

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

3. Aug 1, 2009

### ctpengage

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

4. Aug 1, 2009

5. Aug 1, 2009

### ctpengage

does anyone have a link to an animation

6. Aug 1, 2009

guys?