A block of mass m is pushed against a spring of spring constant k fixed at ne end to a wall. The block ocan side on a frictionless tableas shown in figure. The natural length of thespring is `L_0` and it is compressed ti half its natural length when the block is relesed. Find teh velocity of the block aa s function of its distance x from the wall .

Explanation

When the block is relesed, the spring pushes it towards right. The velocilty of the block increases till the spring acquires its N/Aturla length. Thereater, the block loses contct with the spring and movs with constant velocity.
Initially, the compression of the spring is `L_0/2`, when the distance of the block from the wll becomes x, where `xltL_0` the compression is `(L_0-x)`. Using the principle of conversion of energy.
`1/2 k(L_0/2)^2=1/2k(L_0-x)^2)+1/2mv^2`
Solving this
` v=sqrt(k/m) [L_0^2/4-(L_0-x)^2]^(1/2)`.
When the spring acquires its N/Atural length`x=L_0 and v=sqrt(k/m) L_0/2`. Thereafter, the block contiues with this velocity.