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Which of the following functions of time...

Which of the following functions of time represents (a) simple harmonic motion and (b) periodic motion? Given the period for each case.
i. `Sin omega t - cos omegat` ii. `Sin^(2)omegat`

Text Solution

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`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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