Question

For a particle executing SHM the displacement x is given by x = A cost.
Identify the graph which represents the variation of potential energy (PE) as a
function of time t and displacement x.

• A. I, III
• B. II, IV
• C. II, III
• D. I, IV

Answer 1

The correct option is A I, III

$x=Acost$

$PE=k{x}^2/2$

$PE=k{A}^2(\cos t{)}^2/2=k{A}^2(1+\cos 2t)/4$

At $t=0$ ;$PE$ is maximum and at $t=\pi$ $PE$ is minimum.

Graph I is for $PE$

and when $x=0$ $PE=0$ and when $x=$ maximum or $x=A$ ; $PE=$ $k{A}^2/2$

therefore, Graph III is for PE