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

Answer

B

Explanation

`x= A "cos" (omega t +(pi)/(4))`
`therefore v=(dx)/(dt)= - A omega "sin" (omega t+(pi)/(4))`
v will be maximum, when `"sin" (omega t+ (pi )/(4))=1`
But `"sin" (pi)/(2)=1`,
`therefore omega t+(pi)/(4)=(pi)/(2) therefore omega t =(pi)/(4) or t =(pi)/(4omega)`