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  4. A body is performing simple harmonic motion of amplitude A and time period T . The figure shows position-time graph of the body. At any time t , acceleration of the body is f , then which of the following graphs is/are appropriate? <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-bvtnxp633m9m.png />

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Q. A body is performing simple harmonic motion of amplitude $A$ and time period $T$ . The figure shows position-time graph of the body. At any time $t$ , acceleration of the body is $f$ , then which of the following graphs is/are appropriate?

Question

NTA AbhyasNTA Abhyas 2020Oscillations

Solution:

Since initial phase is $\frac{\pi }{2}$ as per the given graph.
Using the equation of position of SHM $x = A sin \left(\right. \omega t + \frac{\pi }{2} \left.\right)$
$\Rightarrow x = A cos \omega t$
$\Rightarrow $ acceleration $f = \frac{d^{2} x}{d t^{2}} = - A \omega ^{2} cos \omega t$
Which is represented in option third.