Two large non conducting plates having surface charge densities `+sigma` and `-sigma` respectively, are fixed `d` distnce apart. A small test charge `q` of mass `m` is attached to two non conducting springs each of spring constant `k` as shown in the figure. The sum of lengths of both springs in underformed state is `d`. The charge `q` is released from rest with both the springs nondeformed. then charge `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))`