Question

If the potential energy of a harmonic oscillator of mass 2 kg in its equillibrium position is 5 joules and the total energy is 9 joules when the amplitude is one meter, the period of the oscillator (in sec) is:

• A. 1.5
• B. 3.14
• C. 6.28
• D. 4.67

Answer 1

The correct option is B 3.14

Kinetic energy at mean position = elastic potential energy at extreme position $=9J-5J=4J=\frac{1}{2}K{A}^2$
$\Rightarrow k=\frac{4\times 2}{A^2}=\frac{8}{1}=8N/m$
$T=2\pi \sqrt{\frac{m}{k}}=2\pi \sqrt{\frac{2}{8}}=\pi sec=3.14sec$