The function `sin^(4)(omegat)` represents

Options

A. a simple harmonic motion with a period `pi//omega`
B. a simple harmonic motion with a period` 2pi//omega`
C. a period , but not simple harmonic motion with a period `pi//omega`
D. a periodic but not simple harmonic motion with a period `2pi//omega`

Answer

C

Explanation

`y=rsin^(4)(omegat)=rsinomegatxxsin^(3)omegat`
`=rsin omegat[(1)/(4)(3sin omegat-sin 3 omegat)]`
`=r[(3)/(4)sin^(2)omegat-(1)/(4)sinomegat sin 3 omegat ]`
`=(3r)/(4)(1-cos2omegat)`
`=-(r)/(4)xx(1)/(2)[cos(3omegat -omegat)-cos (3omegat+omegat)]`
`=(3r)/(4)(1-cos2omegat)-(r)/(8)[cos 2 omegat -cos 4 omegat]`
It does not represent a SHM but represents a periodic motion with time period
`T=(2pi)/(2omega)=(pi)/(omega)`