Harmonic motion/velocity problem

Hi. I need help with this problem. I tried using vmax = A (k/m)^1/2 and also tried v =-Awsinwt but no luck in getting the answer!

Problem: A 4.7 g bullet is fired horizontally into a 0.50 kg 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-spring system goes into SHM with a frequency of 8.5 Hz and an amplitude of 15 cm. Determine the initial speed of the bullet.

so f = 8.5 = 1/T ; T= .118

Thank youu

Well, in this case, since displacement at t = 0 is 0 and it heads to the right immediately after, the motion actually follows the formula:

x(t) = Asin(ωt)

Then velocity is:

v(t) = Aωcos(ωt)
v(0) = Aω = A(2πf)

**Note that Aω = A*sqrt(k/m), like the equation you listed**

v(0) = (.15 m)(2π)(8.5 1/s)
v(0) = 8.011 m/s

That's both the block and bullet. Use momentum to find the initial speed of the bullet, since the bullet it fired horizontally. m1 corrresponds to the bullet, m2 the block:

m1 * v1 + m2 * v2 = (m1 + m2)v(0)
(4.7 / 1000 kg)v_B + 0 = (4.7 / 1000 + 0.5 kg)(8.011 m/s)
v_B = 860.245 m/s

...which seems unreasonably high. Might just be an unrealistic problem, but hopefully you at least get this process.

EDIT: After some "research", I suppose the answer isn't that unrealistic. Huh.