Question 4: Oscillations

Question

A particle executes SHM with a frequency f. The frequency with which its kinetic energy oscillates is

Accepted Answer

Let displacement, x = A$$\omega$$ sin $$\omega$$t
Velocity, $$v = {{dx} \over {dt}} = A\omega \cos \omega t$$
Kinetic energy of particle in SHM,
$$K = {1 \over 2}m{v^2} \Rightarrow K = {1 \over 2}m{\omega ^2}{A^2}{\cos ^2}\omega t$$
$$ = {1 \over 2}m{\omega ^2}{A^2}\left( {{{1 + \cos 2\omega t} \over 2}} ight)$$ [$$\because$$ $${\cos ^2}	heta  = {{1 + \cos 2	heta } \over 2}$$]
$$ = {1 \over 4}m{\omega ^2}{A^2}(1 + \cos 2\omega t)$$
$$	herefore$$ New angular frequency, $${\omega _K} = 2\omega $$
$$	herefore$$ Frequency of oscillation of kinetic energy = 2f [$$\because$$ $$f = {\omega  \over {2\pi }}$$]

Answer

$${f \over 2}$$

Answer

f

Answer

2f

Answer

4f

Oscillations

A particle executes SHM with a frequency f. The frequency with which its kinetic energy oscillates is

Choose the correct answer: