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`.
