A block of mass m containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall as shown in figure(29-E2). The distance of the bolck from the wall is d. A horizontal electric field E to towards right is switched on. Assuming elastic collisions find the time period of the resulting oscillatory motion. Is it a simple harmonic motion?

Explanation

Here acceleration of block is a `=(qE)/(m)`
Time taken by block to reach wall

`d=1/2((qE)/(m))t^2`
`t=sqrt((2dm)/(qE))`

Velocity at the time of impact is
`v=sqrt(2ad)" or " v=sqrt((2qEd)/(m))`
When the block will rebound time taken by block in coming to rest.
`0=sqrt((2qEd)/(m))-((qE)/(m))t`
`t=((sqrt(2qEd))/(m))/((qE)/(m))=sqrt((2md)/(qE))`
Thus time period of oscillation of block is
`T=2t=2sqrt((2md)/(qE))`
Since the restoring force is independent of x, the displacement from mean position, this is not a simple harmonic motion