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The function `sin^(4)(omegat)` representsA. a simple harmonic motion with a period `pi//omega`B. a simple harmonic motion with a period` 2pi//omega`C. a period , but not simple harmonic motion with a period `pi//omega`D. a periodic but not simple harmonic motion with a period `2pi//omega` |
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Answer» Correct Answer - C `y=rsin^(4)(omegat)=rsinomegatxxsin^(3)omegat` `=rsin omegat[(1)/(4)(3sin omegat-sin 3 omegat)]` `=r[(3)/(4)sin^(2)omegat-(1)/(4)sinomegat sin 3 omegat ]` `=(3r)/(4)(1-cos2omegat)` `=-(r)/(4)xx(1)/(2)[cos(3omegat -omegat)-cos (3omegat+omegat)]` `=(3r)/(4)(1-cos2omegat)-(r)/(8)[cos 2 omegat -cos 4 omegat]` It does not represent a SHM but represents a periodic motion with time period `T=(2pi)/(2omega)=(pi)/(omega)` |
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