A block of mass m attached with a an ideal spring of force constant k is placed on a rough inclined plane having inclination `theta` with the horizontal and coefficient of friction `mu=1//2 tan theta`, Initially the block is held stationary with the spring in its relaxed state, find the maximum extension in the spring if the block is released.

Explanation

`-1/2 kx^(2)+mgx sin theta - mu m g x cos theta = 0 `
`mg sin theta - mu mg cos theta = 1/2 kx`
`x=(mg sin theta)/(k)`