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Swedishfish

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## Homework Statement

A 4 kg block is suspended from a spring with k=500N/m. A .05kg bullet is fired from below into with a speed of 150m/s and comes to rest in the block.

a.)Find the Amplitude of the resulting simple harmonic motion.

b.)What fraction of the original KE of the bullet appears as mechanical energy in the harmonic oscillator?

^^^This is the problem word for word^^^

## Homework Equations

KE=1/2mv^2

F=-ky

U=1/2ky^2

T=2pi(m/k)^1/2

P cons.

E cons.

etc...

## The Attempt at a Solution

Where I am atm is, the problem basically has two parts, the collision which is completely inelastic so Pcons applies and then the compression of the spring and oscillation of the combined masses.

setting up the equations for the collision I apply Pcons.

MblkVblk+MbtVbt=MblkV`blk+MbltV`blt --> Vbb=(MblkVblk+MbtVbt)/(Mblk+Mblt)

-->Vbb=1.85m/s

after the collision having Mbb=4.05 and Vbb=1.85m/s the combined block and bullet mass has

KEbb=113.9J

now I know that at the point of maximum compression of the spring, the mass will be at Vbb=0. So, Applying E cons I set KEbb=Us

113.9J=1/2ky^2 -->227.8=ky^2 --> 227.8/k=y^2 --> (227.8/k)^1/2=y...

Now this is where confusion sets in for me. If I take the problem as I have been, and continue to ignore the hell out of gravity, then there is nothing to dampen the oscillations over time, and I've basically got amplitude since I just solved for maximum compression of the spring. However if I let gravity in the door, things get more complex. This problem is part of a huge packet of problems I'm doing to prep for senior exams so it covers everything from intro on up and this particular problem is located smack in the middle of the medium-difficult ranked intro problems so I don't think the intention here is from me to go charging off with a diff-eq into classical mechanics territory. Since they gave me just masses, velocities and the spring constant I'm kinda thinking this is supposed to be a fairly straight forward energy/momentum problem...

If anyone would look this over and see if there is some thing I'm missing here I'd appreciate it very much as it's been almost 4 years since I took intro. Thanks.

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