Question

A particle is executing simple harmonic motion.Its displacement to amplitude ratio when its kinetic energy is $84\%$ of total energy is

• A. 1 : 16
• B. 2 : 5
• C. 4 : 25
• D. 21 : 25

Answer 1

The correct option is B 2 : 5

Total energy is given by $E_T=\frac{1}{2}m{w}^2{A}^2$
Kinetic energy $K=\frac{1}{2}m{w}^2(A^2-x^2)$
Given : $\frac{K}{E_T}=0.84$
$\therefore$ $\frac{A^2-x^2}{A^2}=0.84$
Or $\frac{x^2}{A^2}=0.16$
$⟹x:A=2:5$