The `x-t` graph of a particle undergoing simple harmonic motion is shown in figure. Acceleration of particle at `t = 4//3 s` is

Options

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

Answer

B

Explanation

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`.
As `x=Asin.(2pi)/(T)t therefore` Acceleration, `a=(d^(2)x)/(dt^(2))=-(4pi^(2))/(T^(2))Asin.(2pi)/(T)t`
At `t=(4)/(3)s`
`a=-(4pi^(2))/(8^(2))xx1xxsin.(2pi)/(8)xx(4)/(3)=-(4pi^(2))/(64)sin.(pi)/(3)=-(sqrt(3)pi^(2))/(32)cms^(-2)`