The initial phase angle observed by a rider in the elevator, taking upward direction to be positive and positive extreme

Question

A 2kg block hangs without vibrating at the bottom end of a spring with a force constant of 400 N/m. The top end of the spring is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of 5 m/s² when the acceleration suddenly ceases at time t = 0 and the car moves upward with constant speed. (g = 10 m/s² )

The initial phase angle observed by a rider in the elevator, taking upward direction to be positive and positive extreme position to have p/2 phase constant, is equal to

A) zero 

(B) p/2 rad 

(C) p rad 

(D) 3p/2 rad

Answer 1

Correct option: (D)  3p/2 rad

Explanation:

Maximum extension the spring from natural position is x. Then mg + ma = kx

Extension of the spring when it is stretched to equilibrium line is x'.

Therefore amplitude A = x –x' = 2.5 cm

If upward direction is taken as positive at t = 0, x = – A

Using x = A sin (wt + f)

 = A sin (wt + f) – A = A sin f

f = 3p/2