For a particle executing S.H.M. the displacement x is given by x … - Vidyadip

MCQ

For a particle executing $S.H.M.$ the displacement $x$ is given by $x = A\cos \omega t$. Identify the graph which represents the variation of potential energy $(P.E.)$ as a function of time $t$ and displacement $x$

✓
$I, III$
B
$II, IV$
C
$II, III$
D
$I, IV$

✓

Answer

Correct option: A.

$I, III$

a
(a) Potential energy is minimum (in this case zero) at mean position ($x = 0$) and maximum at extreme position $(x = \pm A).$
At time $t = 0, x = A,$ hence potential should be maximum.

Therefore graph $I$ is correct. Further in graph $III.$ Potential energy is minimum at $x = 0,$ hence this is also correct.

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