Question

When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude a is

• A. a/4
• B. a/3
• C. a/2
• D. 2a/3

Answer 1

The correct option is C

a/2

$\frac{U}{U_{max}}=\frac{\frac{1}{2}m{\omega }^2{y}^2}{\frac{1}{2}m{\omega }^2{a}^2}\Rightarrow \frac{1}{4}=\frac{y^2}{a^2}\Rightarrow y=\frac{a}{2}$