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 principle of conservationn of momentum. The common velocity after the collisionn is `v/2`. The kinetic energy `=1/2(2m)(v/2)^2=1/4mv^2`. This is also the total energy of vibration as the spring is unstretched at this moment. If the amplitude is A, the total energy can also be written as `1/2kA^2`. Thus
`=1/2kA^2=1/4mv^2, giving A=sqrt(m/(2k))v`.