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The x-t graph of a particle undergoing s...

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

A

`(sqrt3)/(32)pi^(2)cm//s^(2)`

B

`(-pi^(2))/(32)pi^(2)cm//s^(2)`

C

`(pi^(2))/(32)pi^(2)cm//s^(2)`

D

`-(sqrt3)/(32)pi^(2)cm//s^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
The given motion is represented by
`(omega=(2pi)/(T)=(2pi)/(8)=(pi)/(4))`
`x=1sin((pi)/(4)t)`,`(d^(2)x)/(dt^(2))=(-pi^(2))/(16)sin (pi//4)t`
At `t=4//3s`,`(d^(2)x)/(dt^(2))=-(sqrt3)/(32)pi^(2)cm//s^(2)`
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