Question

A block of mass $m$ containing a net positive charges $q$ is placed on a smooth horizontal table which terminates in a ventricles wall as shown in figure $\left(29.E2\right)$. The distance of the block from the wall is $d$. A horizontal electric field $E$ towards right is switched on. Assuming elastic collisions $($ if any$)$ find the time periods of the resulting oscillatory motion. Is it a simple harmonic motion?

Answer 1

Acceleration of block is $a=\frac{qE}{m}$

Time taken to reach the wall is equal to time taken from wall to reach the starting position since the collision is elastic.

$d=\frac{1}{2}\frac{qE}{m}{t}^2$

$⟹t=\sqrt{\frac{2dm}{qE}}$

Hence, time taken to reach initial point is $T=2t$

Time of oscillation$=T=\sqrt{\frac{8dm}{qE}}$

Since, acceleration is constant ,it is not simple harmonic.