InterviewSolution
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InterviewSolution
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The displacement of a particle is repersented by the equation `y=3cos((pi)/(4)-2omegat)`. The motion of the particle is(b) (c) (d)A. non-periodicB. periodic but not simple harmonicC. simple harmonic with period `2pi//omega`D. simple harmonic with period `pi//omega` |
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Answer» Correct Answer - B (b) Given , equation of motion is `y="sin"^(3)omegat=(3 "sin"omegat-4"sin"omegat)//4" "[because "sin"3 theta =3 "sin"theta-4"sin"^(3)theta]` `implies (dy)/(dt)=[(d)/(dt)(3"sin"omegat)-(d)/(dt)(4 "sin"omegat)]//4` `4(dy)/(dt)=3omega"cos"omegat-4xx[3omega"cos"3 omegat]` `implies4xx(d^(2)y)/(dt^(2))=-3omega^(2)"sin"omegat+12 omega^(2)"sin"omegat` `implies(d^(2)y)/(dt^(2))=-(3omega^(2)"sin"omegat+12omega^(2)"sin"3omegat)/(4)` `implies(d^(2)y)/(dt^(2))` is not proportional to y. Hence, motion is not SHM. As the expression is involing sine function ,hence it will be periodic. |
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