Question

For a particle executing simple harmonic motion, the displacement x is given by x = A cos wt. 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)

II, IV

Answer 2

Given: $x = A\cos\omega t$

Potential energy,

$U = \frac{1}{2}m\omega^{2}x^{2} = \frac{1}{2}m\omega^{2}A^{2}\cos^{2}\omega t$

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.