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

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

F_s=-kx
a=-(k/m)x
PE_s= .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?

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.