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 block 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

The block does not undergo SHM.
` D=ut+1/2at^2 `
` Here, u=0, a=(qE)/m `
` t_1=sqrt((2d)/a)=sqrt((2dm)/(qE)) `
` v=u+at=(qE)/m sqrt((2dm)/(qE) )`
` Again, u=v+at_2=0 `
` or t_2=v/a=(qE)/m sqrt((2dm)/(qE))/a=sqrt((2dm)/(qE)) `
` Total time `
` t=t_1+t_2=2=sqrt((2dm)/(qE) )`
` =sqrt((8dm)/(qE))`.