Question

Two simple harmonic oscillators with amplitudes in the ratio $1:2$ are having the same total energy. The ratio of their frequencies is

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

Answer 1

The correct option is C $2:1$

$\frac{\frac{1}{2}m{w}_1^2{A}_1^2}{\frac{1}{2}m{w}_2^2{A}_2^2}=1Here\frac{A_1}{A_2}=\frac{1}{2}$
$\frac{w_1}{w_2}=\frac{2}{1}$