A particle is executing SHM given by `x = A sin (pit + phi)`. The initial displacement of particle is `1 cm` and its initial velocity is `pi cm//sec`. Find the amplitude of motion and initial phase of the particle.

Answer

A, B, C, D

Explanation

`x = A sin (pit + phi)`
At `t = 0 , x= 1 cm rArr A sinphi = 1"…."(i)`
Velocity `v = (dx)/(dt) = piA cos (pit + phi)`
At `t = 0 pi = piA cos phi rarr Acosphi = 1"……."(ii)`
from `(i)` & `(ii) A^(2) (sin^(2)phi + cos^(2) phi) = 1 + 1`
`rArr A = sqrt(2) cm` and `tanphi = 1 rArr phi = (pi)/(4) rad`