Question

A particle is oscillating simple harmonically from its equilibrium position. Then the ratio of kinetic and potential energy of the particle at time $T/12$ is ($T$ - time period):

• A. $2:1$
• B. $3:1$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is B $3:1$

$PE=\frac{1}{2}k{x}^2$
$k=m{\omega }^2$
$PE=\frac{1}{2}m{\omega }^2{x}^2$
$KE=\frac{1}{2}m(A^2-x^2){\omega }^2$
$x=Asin{30}^o$ Assume $\theta ={30}^{\circ }$
$x=\frac{A}{2}$
$\frac{KE=\frac{1}{2}m(A^2-\frac{A^2}{4}){\omega }^2}{PE=\frac{1}{2}m{\omega }^2\times \frac{A^2}{4}}$
$\frac{KE}{PE}=\frac{3}{1}$