Which of the following equations does not rep | vedclass

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(D) The standard differential equation for Simple Harmonic Motion $(S.H.M.)$ is given by $\frac{d^2y}{dt^2} = -\omega^2 y$.For $y = a \sin \omega t$,$

Vedclass · Accepted Answer

$y = a 	an \omega t$

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(D) The standard differential equation for Simple Harmonic Motion $(S.H.M.)$ is given by $\frac{d^2y}{dt^2} = -\omega^2 y$.For $y = a \sin \omega t$,$\frac{d^2y}{dt^2} = -a \omega^2 \sin \omega t = -\omega^2 y$. This satisfies the condition.For $y = a \cos \omega t$,$\frac{d^2y}{dt^2} = -a \omega^2 \cos \omega t = -\omega^2 y$. This satisfies the condition.For $y = a \sin \omega t + b \cos \omega t$,this is a linear combination of two $S.H.M.$ functions with the same frequency,which also results in an $S.H.M.$For $y = a 	an \omega t$,the function is not bounded (it goes to infinity at $\omega t = \pi/2$),and it does not satisfy the differential equation $\frac{d^2y}{dt^2} = -\omega^2 y$. Therefore,it does not represent $S.H.M.$

Which of the following equations does not represent a simple harmonic motion?

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