A block of mass m is pushed against a spring of spring constant k fixed at one end to a wall.The block can slide on a frictionless table as shown in the figure. The natural length of the spring is `L_0` and it is compressed to one fourth of natural length and the block is released.Find its velocity as a function of its distance (x) from the wall and maximum velocity of the block. The block is not attached to the spring.

Explanation

`(1)/(2)k((3L_0)/(4))^2=(1)/(2)mv^2+(1)/(2)k(L_0-x)^2`
when `xltL_0`
`impliesv=sqrt((k)/(m)[((3L_0)/(4))^2-(L_0-x)^2`])`
when `xgeL_0`
velocity is maximum when `x=L_0` and
`v_(max)==(3L_0)/(4)sqrt((k)/(m))`