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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) sinomegat-cosomegat (2) sin^(2)omegat |
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Answer» Solution :(a) `sinomegat-cosomegat` `=sinomegat-sin(pi//2-omegat)` `=2cos(pi//4)sin(omegat-pi//4)` `=sqrt2sin(omegat-pi//4)` This function represents a simple harmonic motion having a period `T=2pi//omega` and a PHASE angle `(-pi//4)` or `(7pi//4)` (b) `sin^(2)omegat` `=1//2-1//2cos2omegat` The function is periodic having a period `T = pi//omega`. It also represents a harmonic motion with the point of equilibrium OCCURRING at `1//2` INSTEAD of zero. |
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