A partical slides back and forth between two inclined friction lessplanes.

a. If h is the initial height of the partical, the period of oscillation……
b. Is the motion oscillatory? Is it SHM?

Explanation

Restoring force `F = mg sin alpha`
`F = mg (y)/( r)`

As far as motion a is constant motion is not SHM. As motion is restriched between two point and separted itself hence oscillatory.
Time taken for the block to side down a height R
`(h)/(sin alpha) = (1)/(2) g sin alpha t^(2)`
`t^(2) = (2 h)/(R) (1)/(sin^(2) alpha)`
`t = (1)/(sin alpha) sqrt((2h)/(g))`
Hence period,
`4t = ((4)/(sin alpha) sqrt((2h)/(g)))`