The instantaneous displacement of a simple pendulum oscillator is given by `x= A cos (omegat+ pi / 4 )`Its speed will be maximum at time

Options

A. `t=(pi)/(omega)`
B. `t=(2pi)/(omega)`
C. `t=(pi)/(4 omega)`
D. `t=(omega)/(2pi)`

Answer

C

Explanation

`x = A "cos" (omega t+ pi //4)`
`therefore (dx)/(dt) = - A omega "sin" (omega t+(pi)/(4))`
The speed is maximu when `(omega t+(pi)/(4))=(pi)/(2)`
or `omega t + (pi)/(2)-(pi)/(4)=(pi)/(4) therefore t =(pi)/(4omega)`