The following figure shows a block of mass m suspended from a fixed point by means of a vertical spring. The block is oscillatting simple harmonically and carries a charge q. There also exists a uniform electric field in the region. Consider four different cases. The electric field is zero in case 1, `mg//q` downward in case 2, `mg//q` upward in case 3, and `2mg//q` downward in case 4. The speed at mean position is same in all cases. Select the correct alternative (s).

Options

A. Time periods of oscillation are equal in case 1 and case 3.
B. Amplitudes of displacement are same in case 2 and case 3.
C. The maximum elongation (increment in length from natural length) is maximum in case 4.
D. Time periods of oscillation are equal in case 2 and case 4.

Answer

A, B, C, D

Explanation

a.,b.,c.,d.
(a) Only equilibrium position changes. Time period remains same `T=2pisqrt(m//K)`.
(b) `(1)/(2)kx^(2)=(1)/(2)mv^(2)`
So `v` at mean position is same amplitude will be same.
(c) In case `4` equilibrium psotion is `x_(0)=3mg//k`.