Question

A particle of mass 2 kg moves in simple harmonic motion and its potential energy U varies with position x as shown. The period of oscillation of the particle is:

• A. $\frac{2\pi }{5}$ s
• B. $\frac{2\sqrt{2}\pi }{5}$ s
• C. $\frac{\sqrt{2}\pi }{5}$ s
• D. $\frac{4\pi }{5}$ s

Answer 1

The correct option is D $\frac{4\pi }{5}$ s

$\frac{1}{2}k{A}^2=1.0$
$\frac{1}{2}k{\left(0.4\right)}^2=1.0$
or $k=12.5$ or $\frac{25}{2}$ N/m
$T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{\frac{2}{\frac{25}{2}}}=\frac{4\pi }{5}$ s