Block of mass `2 m` is given `v_(0)` towards the right. If `L` is the natural length of spring constant `k`, find the maximum elongation of the spring.

Explanation

As the blocks move , the spring is extended.
Due to the force , speed of `2 m` decreases and that of `m` increases. At the time of maximum elongation , the block moves with same veloctiy .
`x_(0)`: maximum elongation
`m xx 0 + 2mv_(0) = mv + 2 mv`
`rArr v = (2v_(0))/(3)`
`(1)/(2) xx 2m v_(0)^(2) = (1)/(2)(m + 2m) v^(2) + (1)/(2) kx_(0)^(2)`
`x_(0) = sqrt((2 m v_(0)^(2))/(3k)) = v_(0) sqrt((2m)/(3k))`