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The displacement of a particle is repres...

The displacement of a particle is represented by the equation `y=3cos((pi)/(4)-2omegat).`
The motion of the particle is

A

simple harmonic with period `2//omega`

B

simple harmonic with perioed `pi//omega`

C

periodic but not simple harmonic

D

non-periodic.

Text Solution

Verified by Experts

The correct Answer is:
B
`y = 3 cos((pi)/(4) - 2omegat)`
`therefore v = (dy)/(dt) = 3(-2)omega[-sin((pi)/(4)-2omegat)]`
` = 6omega((pi)/(4) -2omegat)`
And `a = (dv)/(dt) = -12omega^(2)(cos(pi)/(4) - 2omegat)`
` = -4omega^(2)[3cos((pi)/(4) - 2omegat)]`
` = -4omega^(2)y`
or `a prop -y`
Hence the motion is S.H.M. having time period
` T = (2pi)/(2omega) = (pi)/(omega)`
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