The displacement of a linear simple harmonic oscillator is given by `y = "sin"(pi)/(2)[(t)/(2)+(1)/(2)]` cm. The maximum acceleration of the oscillator in `cms^(-2)` is

Options

A. `(pi)/(4)`
B. `(pi^(2))/(4)`
C. `(pi^(2))/(8)`
D. `(pi^(2))/(16)`

Answer

D

Explanation

`y= "sin" ((pi t)/(4)+(pi)/(4))`
Comparing with `y=A "sin" (omega t+ phi)`, we get
`A=1, omega=(pi)/(4)`
`therefore " maximum acceleration " =omega^(2)A =(pi^(2))/(16)xx1=(pi^(2))/(16)`