Question

The displacement of linear harmonic oscillator is given by $x=A\cos \omega t$. The curves showing the variation of the potential energy with t and x(see figure) are displayed respectively by.

• A. I and III
• B. I and IV
• C. II and III
• D. II and IV

Answer 1

The correct option is A I and III

Potential Energy, $P.E=\frac{1}{2}m{\omega }^2{x}^2$

$\omega =2\pi f$

$f=\frac{1}{T}$

$\therefore {\omega }^2=\frac{4{\pi }^2}{T^2}$

$\therefore P.E=\frac{1}{2}m\frac{4{\pi }^2{x}^2}{T^2}=2{\pi }^{2}m\frac{x^2}{T^2}=U$