The oscillation of a body on a smooth horizontal surface is represented by the equation $x= Acos$$\omega t$
where $x=$ displacement at time $t$
$\omega =$ frequency of oscillation
Which one of the following graphs shows correctly the variation $a$ with $t$ ?
Here $a=$ acceleration at time $t$
$T=$ time period
AIPMT 2014, Medium
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$ Here, X =A \cos \omega t$
$ \therefore \text { Velocity, } v =\frac{d X}{d t}=\frac{d}{d t}(A \cos \omega t)$
$ =-A \omega \sin \omega t $
$ \text { Acceleration, } a =\frac{d v}{d t}=\frac{d}{d t}(-A \omega \sin \omega t) $
$=-A \omega^{2} \cos \omega t$
Hence the variation of $a$ with $t$ is correctly shown by graph$(c).$
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