Question

For a particle executing simple harmonic motion, the displacement x is given by x = A cos$\omega t$. 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

Given $x=Acos\omega t$ As a function of x, the PE is given by
$PE=\frac{1}{2}m{\omega }^2{x}^2$ At x = 0, PE = 0. Hence the correct graph is III. As a function of t, the PE is given by $PE=\frac{1}{2}m{\omega }^2(Acos\omega t{)}^2=\frac{1}{2}m{\omega }^2{A}^{2}co{s}^2\omega t$
At t = 0, PE is maximum equal to $\frac{1}{2}m{\omega }^2{A}^2$ Hence the correct graph is I. Thus, the correct choice is (a)