Question

For a particle executing simple harmonic motion, the displacement x is given by $x=Acos\omega t$. Identify the graph, which represents the variation of potential energy (U) as a function of time t and displacement x.

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

Answer 1

Answer: (D)

Given : $x=Acos\omega t$
Potential energy, $U=\frac{1}{2}m{\omega }^2{x}^2=\frac{1}{2}m{\omega }^2{A}^{2}co{s}^2\omega t$
On plotting a graph between potential energy U and time t, we shall get a curve II and graph between U and x we shall get curve IV.