Question

A 0.940 kg block is attached to a horizontal spring with spring constant 2550 N/m. The block is at rest on a frictionless surface. A 7.90 g bullet is fired into the block, in the face opposite the spring, and sticks.
What was the bullet's speed if the subsequent oscillations have an amplitude of 10.2 cm?

Answer 1

The spring's potential energy at maximum compression (when X is the amplitude of viration) equals the initial kinetic energy at zero deflection, after the bullet hits.

Use that fact to get the initial velocity of the vibrating Bullet-Block combo.

Then use conservation of momentum to get the velocity of the bullet before impact.