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Question
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant):
sin ωt – cos ωt
Solution
Simple harmonic
The given function is:
`sin omega"t" - cos omega"t"`
`= sqrt2[1/sqrt2 sin omega"t" - 1/sqrt2 cos omega"t"]`
`=sqrt2[sin omega"t" xx cos pi/4 - cos omega"t" xx sin pi/4]`
`= sqrt2 sin (omega"t" - pi/4)`
This function represents SHM as it can be written in the form: `asin (omegat + phi)`
Its period is : `(2pi)/omega`
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