Question

When a body is in SHM, match the statements in Column A with that in Column B
Column A Column B
a) Velocity is maximum e) At half of the amplitude
b) Kinetic energy is f) At the mean position
3/4th of total energy
c) Potential energy is g) At extreme position
3/4th of total energy
d) Acceleration is h)At $\sqrt{3}/2$ times amplitude
maximum

• A. a-f, b-e, c-h, d-g
• B. a-e, b-f, c-g, d-h
• C. a-g, b-h, c-e, d-f
• D. a-h, b-e, c-f, d-e

Answer 1

The correct option is A a-f, b-e, c-h, d-g

Velocity is maximum at mean position
$v_{max}=\omega A$
Kinetic
Energy $KE=\frac{1}{2}m{v}^2=\frac{1}{2}m{\omega }^2(A^2-x^2)$
Total
Energy $TE=\frac{1}{2}m{\omega }^2{A}^2$
$KE=\frac{3}{4}\times TE;A^2-x^2=\frac{3}{4}{A}^2$
$x^2=\frac{A^2}{4};x=\frac{A}{2}$
Potential
$PE=\frac{1}{2}m{\omega }^2{x}^2=\frac{3}{4}\times \frac{1}{2}m{\omega }^2{A}^2$
Energy
$x=\frac{\sqrt{3}}{2}A$
Acceleration is maximum at extreme position
$a_{max}=-{\omega }^{2}A$