In a horizontal spring - mass `m` is released after being displaced toward right by same distance `t = 0` an a frictionless surface The phase angle of motion in ratio when it is first time passing through equlibrium possition is equal to

Options

A. `(pi)/(2)`
B. `pi`
C. `(3pi)/(2)`
D. 0

Answer

B

Explanation

Phase of the motion is `(omega t + phi)`
Using `x = A sin (omega t + phi)` and `V = Aomegacos(omega + phi)`
for condition at `t = 0 rarr x = A` and `V = 0` then `phi = (pi)/(2)` when it passes equilibrium for the first time
`t = (T)/(4)`
Phase `(2pi)/(T).(T)/(4) + (pi)/(2) = pi`