The left block in filgure collides inelastically with the right block and sticks to it. Find the amplitude of the resulting simple harmonic motion.

Explanation

Assuming the collision to last for a small interval only we can apply the principal of conservation of momentum. The common velocity after collision is `v//2`. The kinetic energy is
`(1)/(2) (2 m) (y/(2))^(2) = (1)/(4) mv^(2)`
Tjhis is also the tortal energy of vibration as the spring is unsteteched at this momentum. If the amplitude is A, the total energy can also be written as `(1//2) kA^(2)`. Thus.
`(1)/(2) kA^(2) = (1)/(4) mv^(2)`
`A = sqrt((m)/(2 K)) v`