Question

A simple pendulum is oscillating with amplitude ‘$A$’ and angular frequency ‘$ω$’. At displacement ‘$x$’ from mean position, the ratio of kinetic energy to potential energy is

• A. $\frac{x^{2}}{A^{2}-x^{2}}$
• B. $\frac{x^{2}-A^{2}}{x^{2}}$
• C. $\frac{A^{2}-x^{2}}{x^{2}}$
• D. $\frac{A-x}{x}$

Answer 1

Answer: (C)

Kinetic energy of pendulum oscillating with amplitude $A$ and angular frequency $\omega$ at displacement $x$ from mean position is
$KE =\frac{1}{2} k\left(A^{2}-x^{2}\right)$

Potential energy of pendulum at displacement $x$ from mean position is
$P E=\frac{1}{2} k x^{2}$
$\therefore \,\,\,\frac{K E}{P E}=\frac{\frac{1}{2} k\left(A^{2}-x^{2}\right)}{\frac{1}{2} k x^{2}}=\frac{A^{2}-x^{2}}{x^{2}}$