Two large insulating plates having surface charge densities `+sigma` and `+sigma` are fixed at a distance d frome each other . A small test charge q of mass m is attached to two identical spring as show in the fingure . The charge q is now released from rest with springs in natural lenth . Then q will (Neglect gravity)

Options

A. performs `SHM` with angular frequency `sqrt((2k)/(m))` and amplitude `(sigmaq)/(kepsilon_(0))`.
B. perform `SHM` with angular freqeuncy `sqrt((2k)/(m))` and amplitude `(eq)/(2kepsilon_(0))`
C. not perform `SHM`, but will execute periodic motion.
D. remain stationary.

Explanation

The electrostatic force on charge is constant, hence it does not effect the time period of spring `+` particle system.
`therefore omega=sqrt((2K)/(m))`
Initially the charge is at rest, i.e. at extreme position.
The equilibrium position, shall be at a distance `A` towards right, where `A` (by definition) is amplitude of vibration.
`therefore 2kA=(sigma)/(epsilon_(0))` or `A=(sigmaq)/(2kepsilon_(0))`