Question

When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is ‘n’, the frequency of the kinetic energy is

• A. n/2
• B. n
• C. 2n
• D. 4n

Answer 1

Answer: (C)

2n

Answer 2

K.E. = $\frac{m\omega^{2}}{2}(A^{2} - y^{2})$ =$\frac{m\omega^{2}}{2}\lbrack A^{2} - (A\sin(\omega t + \varphi))^{2}\rbrack$

= $\frac{m\omega^{2}}{2}\lbrack A^{2} - A^{2}\sin^{2}(\omega t + \varphi)\rbrack$

= $\frac{m\omega^{2}A^{2}}{2}\lbrack\cos^{2}(\omega t + \varphi)\rbrack$

= $\frac{m\omega^{2}A^{2}}{4}\lbrack 1 + \cos(2\omega t + 2\varphi)\rbrack$

∴ Frequency = $\frac{2\omega}{2\pi}$ = 2n