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)/(16)xx 1 = (pi^(2))/(16)`