A particle executes simple harmonic motion with a frequency f. The frequency with which the potential energy oscillates is:

Question

A particle executes simple harmonic motion with a frequency f. The frequency with which the potential energy oscillates is: (A)  f  (B)  f/2  (C)  2f  (D) 0

Tardigrade Admin · Accepted Answer

If x=A text sin text ω t Then, PE=(1/2)mA2ω 2 sin 2ω t ∴ PE=(1/2)mA2ω 2( (1- cos 2ω t/2) ) ∴ ω' =2ω Or 2π f'=2× 2π f f'=2f

Q. A particle executes simple harmonic motion with a frequency $f$ . The frequency with which the potential energy oscillates is:

$f$

$f /2$

$2 f$

0

If $x = A s in ω t$
Then, $PE = \frac{1}{2} m A^{2} ω^{2} sin^{2} ω t$
$∴$ $PE = \frac{1}{2} m A^{2} ω^{2} (\frac{1 - c o s 2 ω t}{2})$
$∴$ $ω^{'} = 2 ω$
Or $2 π f^{'} = 2 \times 2 π f$
$f^{'} = 2 f$

Q. A particle executes simple harmonic motion with a frequency f. The frequency with which the potential energy oscillates is:

f

f/2

2f

0

If x=Asinωt Then, PE=21​mA2ω2sin2ωt ∴ PE=21​mA2ω2(21−cos2ωt​) ∴ ω′=2ω Or 2πf′=2×2πf f′=2f

Q. A particle executes simple harmonic motion with a frequency $f$ . The frequency with which the potential energy oscillates is:

$f$

$f /2$

$2 f$

If $x = A s in ω t$
Then, $PE = \frac{1}{2} m A^{2} ω^{2} sin^{2} ω t$
$∴$ $PE = \frac{1}{2} m A^{2} ω^{2} (\frac{1 - c o s 2 ω t}{2})$
$∴$ $ω^{'} = 2 ω$
Or $2 π f^{'} = 2 \times 2 π f$
$f^{'} = 2 f$