The following figure-I .427 shows a block of mass m suspended from a fixed point by means ofa vertical spring. The block is oscillating simple harmonically and carries a charge q. There also exists a uniform electric field in the space. Consider four different cases. The electric field is zero, in case-I, `E= mg//q` downward in case-2, `E = mg// q` upward in case-3 and `E = 2mg//q` downward in case-4. The speed at mean position of block is same in all cases. Select which of the following statements is/ are correct :

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`.