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 conservation momentum. The common velocity after the collision is `(v)/(2)`. The kinectic energy `= (1)/(2)(2m) ((v)/(2))^(2) = (1)/(4) mv^(2)`. This is also the total energy of viberation as the spring isunstretched at this moment. If the amplitude is `A`, the total energy cen also be written as `(1)/(2)kA^(2)`. Thus,
`(1)/(2)kA^(2) = (1)/(4)mv^(2)`, giving `A = sqrt((m)/(2k))v`.