A block of mass m carrying a net positive charge q is positioned on a smooth horizontal table that ends at a vertical wall, as shown in the figure. The block's distance from the wall is d . A horizontal electric field E directed towards the right is turned on. Assuming any collisions to be elastic, determine the time period of the ensuing oscillatory motion and state if it is simple harmonic.

Step-by-step solution

Force on the block, F = qE Acceleration of the block, a = qE m Let t be the time taken by the block to reach the wall. Using the second equation of motion: d = 1 2 at^2 t = 2d a = 2md qE Since the collision with the wall is elastic, the block rebounds with the same speed. The electric force continues to act towards the right, retarding the block's motion to the left. It will take the same time t to come to rest at its initial position. Total time period of oscillation, T = 2t = 2 2md qE = 8md qE For a motion to be