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For a particle executing simple harmonic motion, the displacement x is given by $x = A \cos ω t .$ Identify the graphs that represent variation of potential energy (U) as a function of time (t) and displacement (x)

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(I), (III)

(II), (IV)

(I), (IV)

(II), (III)

answer is A.

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Detailed Solution

$\begin{array}{l} U = \frac{1}{2} m ω^{2} \times^{2} \frac{1}{2} m ω^{2} A^{2} \cos^{2} ω t \\ A t t = 0, U \neq 0 \\ A t X = 0, U \neq 0 \end{array}$

So, the correct graphs are (1) and (3)

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