The (x - t) graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at `t = 4//3 s` is
.

Options

A. `(sqrt(3))/(32)pi^(2)cm//s^(2)`
B. `(-pi^(2))/(32)cm//s^(2)`
C. `(pi^(2))/(32)cm//s^(2)`
D. `(-sqrt(3))/(32)pi^(2)cm//s^(2)`

Answer

D

Explanation

Refer to figure., at time `t=0s,` the displacement `x=0`. Therefore, the curve is a sinusoidal curve. It represents SHM whose amplitude, `a=1cm and T=8s.`
`x=asin ((2pi)/(T))t`
Acceleration `=(pi^(2))/(T^(2))asin((2pi)/(T))t`
At, `t=(4)/(3)s.`
Acceleration `=-(4pi^(2))/(8^(2))xx1xxsin((2pi)/(8))xx(4)/(3)`
`=-(4pi^(2))/(64)sin ((pi)/(3))=-(4pi^(2))/(64)xx(sqrt(3))/(2)`
`=-(sqrt(3)pi^(2))/(32)cm//s^(2)`)