How Do You Determine Spring Compression in Harmonic Motion?

[zbirdie]

Homework Statement

A 2 kg block is dropped from a height of .45 m above an uncompressed spring. The springs k value is 200 N/m, and has negligible mass. The block strikes the end of the spring and sticks to it.

a) determine the speed of the block at the instant it hits the end of the spring.

Ok, I did this, I am fairly certain my answer is correct, because I checked it using conservation of energy. Anyhow, I got that the speed of the block at the instant it hits the end of the spring was V=2.970 m/s

b) Determine the period of the simple harmonic motion that ensues.

OK, did this, using the equation for Ts, and got that T=.628s.

c) Determine the distance that the spring is co0mpressed at the instant the speed of the block is maximum.

Ok, this is the part where I need help. I want to use conservation of energy, and I know that I can, because although the spring and the block collide, the spring is massless, so no heat is created.

The relevant equation for this part is (I think) Vmax=wwA. For w, I plugged in 2pi/T=10rad/s. Then for Vmax I used 2.970m/s. This is the main part I am having doubts about. My logic was that since this is the velocity right when the block hits the uncompressed spring, there is no SPE, so there fore the velocity is the maximum it could ever be. Anyways, using this method, I got that the amplitude, and thus the compression of the spring at the highest velocity of the block, was .03m, or 3cm. I don't know if this is right, so I would greatly appreciate reassurance/guidance on how to do this correctly. Thank you

 

[Carid]

c) Determine the distance that the spring is co0mpressed at the instant the speed of the block is maximum.

Surely the block is at its maximum speed just as it hits the top of the spring and therefore the compression is zero.

If on the other hand the word "maximum" should read "minimum", then its just a question of equating the kinetic energy of the block before impact to the work done (i.e. force * distance) compressing the spring to halt the block.