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Which of the following functions of time...

Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic? Give the period for each case.
(1) `sin omega t = cos omega t`
(2) `sin^(2) omega t`

Text Solution

Verified by Experts

`sin omega t + cos omegat `
`= sin omegat + sin ((pi)/(2) - omegat )`
`= 2 sin ((pi)/(4)) cos (omegat-(pi)/(4))` ( using `sin C + sin D = 2 sin . (C+D)/(2) cos . (C-D)/(2))`
`= 2 xx (1)/( sqrt(2)) cos ( omegat - (pi)/( 4))`
`= sqrt(2) cos ( omegat -(pi)/( 4))`
This function represent a SHM having period `T= (2pi)/( omegat) ` and phase `( - (pi)/( 4)) `or `( (7pi)/(4))`
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