Question

Assistance with a Simple Harmonic Motion problem?..

Answer 1

the energy in the bullet will be conserved. it might be converted into other forms of energy (certainly you can imagine the bullet bob heating up somewhat, and there being some sound) but i think these types of question require you to assume that the energy lost in that way is de minimis.

THEREFORE you should proceed on the basis that, for all practically purposes, the kinetic energy of the bullet just before the collision becomes the combined kinetic energy of the bullet and bob that are now joined together.

this allows you to answer the remaining questions provided you know the relevant energy equations - for kinetic energy and potential energy. i assume that you do.

pls ask if there is a problem.