InterviewSolution
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InterviewSolution
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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` |
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Answer» i. `sin omegat - cos omegat = sqrt(2) [(1)/(sqrt(2))Sin omegat-(1)/(sqrt(2))Cos omegat]` `= sqrt(2) [Sin omegat cos.(pi)/(4) -cos omega t "sin"(pi)/(4)]` `= sqrt(2) sin (omegat - pi//4]` This fuctions represent a simple harmonic motion having a period `T = (2pi)/(omega)` and a phase angle `(-pi//4)` or `(7pi//4)`. ii) `Sin^(2) omegat =(1-cos.(2omegat))/(2) = (1)/(2) -(1)/(2) cos (2 omegat)` The function is periodic having a period `T = pi//omega` It is not `SHM` Note: If displacement of a particle moving along straight line is given by `y = A sin^(2)omegat` then it represents `SHM`. |
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