Question

A loaded vertical spring executes simple harmonic oscillations with period of 4 s. The difference between the kinetic energy and potential energy of this system oscillates with a period of

• A. 8 s
• B. 1 s
• C. 2 s
• D. 4 s

Answer 1

The correct option is C

2 s

$K.E.=\frac{1}{2}n{\omega }^2{A}^{2}co{s}^2\omega t$

$P.E.=\frac{1}{2}m{\omega }^2{A}^{2}si{n}^2\omega t$

$K.E.-P.E.=\frac{1}{2}m{\omega }^2{A}^2[co{s}^2\omega t-si{n}^2\omega t]$

$=\frac{1}{2}m{\omega }^2{A}^{2}cos2\omega t$

$\therefore$ Angular frequency = 2 $\omega$