Two blocks `A` and `B` of masses `m` and `2m` respectively are connected together by a light spring of stiffness `k` and then placed on a smooth horizontal surface. The blocks are pushed towards each other such that spring gets compressed by a length `x_(0)` and then released from rest. Find the work done on the block `A` by the spring, by the time the spring acquires its natural length.

Explanation

from `COM`
`mv_(A)=2mv_(B)`
`rArr v_(B)=(v_(A))/(2)`
from `COE`
`(1)/(2)kx_(0)^(2)=(1)/(2)mv_(A)^(2)+(1)/(2)xx2m(v_(A)^(2))/(4)=(1)/(2)mv_(A)^(2)(1+(1)/(2))`
`rArr(1)/(2)kx_(0)^(2)=(1)/(2)mv_(A)^(2)xx(3)/(2)rArr(1)/(2)mv_(A)^(2)=(kx_(0)^(2))/(3)`