Two blocks of masses `m` and `2m` compress a spring of spring constant k by `x_(0)` and blocks are a connected by a thread and placed on a smooth surface as shown. Now , thread is burned. Find the speed of each block when the spring attains its normal length `L`.

Explanation

By the momentum conservation
`0 = -mv_(1) + 2mv_(2) rArr v_(1) = 2v_(2)`
By the energy conservation
`(1)/(2) k x_(0)^(2) = (1)/(2) mv_(1)^(2) + (1)/(2) xx 2mv_(2)^(2)`
`kx_(0)^(2) = m(2v_(2))^(2) + 2 mv_(2)^(2) = 6 mv_(2)^(2)`
`v_(2) = sqrt((kx_(0)^(2))/(6 m))`
`v_(1) = 2v_(2) = 2 sqrt((kx_(0)^(2))/(6 m))`