# Simple Harmonic Motion (Bullet fired into a block attached to spring)

1. May 4, 2011

### fluffymastr

1. The problem statement, all variables and given/known data

A 5g bullet is fired horizontally into a 0.50kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring, retains the bullet and moves forward, compressing the spring. The block-bullet system goes into SHM with a frequency of 9Hz and amplitude of 15cm.

A) Determine the speed of the bullet

2. Relevant equations

Fs=-kx
a=-(k/m)x
PEs= .5kx2
v=±[(k/m)(A2-x2)].5
T=2π(m/k).5

3. The attempt at a solution

I wasn't sure how to even approach this but I think I need to determine the spring constant k using a form of T=2π(m/k).5.

So:
T=2π(m/k).5
T2=4π2(m/k)
T2=4π2(m/k)
k=(4π2m)/(T2)
k=(4π2(.5kg+.005kg))/(92)
k=.24613kg/s2

Then plug that into:
v=±[(k/m)(A2-x2)].5
v=±[(.24613/.505)(.152-02)].5
v=.1047m/s

I have NO IDEA if I am right or not. Anyone want to confirm or deny?

2. May 4, 2011

### ideasrule

The frequency is 9 Hz, not the period.
That would be right if you used the right value of k. The equation comes from the conservation of energy, which says that 1/2*k(A^2-x^2)=1/2mv^2.