A pendulum is undergoing SHM with frequency f What is the frequency of its kinetic energy ?

$\frac{f}{2}$

2 f

3 f

4 f

Solution

2 f

Suppose A particle in s.H.M follows the equation

$X = A \sin ωt \Rightarrow \frac{dX}{dt} = V = A ω cosωt So, kinetic energy = \frac{1}{2} {mv}^{2} = \frac{1}{2} m A^{2} ω^{2} \cos^{2} ωt Now if a particlewould have been moving following such equation i . e Y = \frac{1}{2} m A^{2} ω^{2} \cos^{2} ωt Y = \frac{1}{4} m A^{2} ω^{2} (2 \cos^{2} ωt) Y = \frac{1}{4} m A^{2} ω^{2} (\sin 2 ωt + 1) Y - \frac{1}{4} m A^{2} ω^{2} = \frac{1}{4} m A^{2} ω^{2} \sin 2 ωt y = \frac{1}{4} m A^{2} ω^{2} \sin 2 ωt (since y = Y - \frac{1}{4} m A^{2} ω^{2} = constant) \frac{1}{4} m A^{2} ω^{2} - Amplitude \sin 2 ω t - has been doubled so frequency is doubled as well$

Some More Questions From Oscillations Chapter

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

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The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

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Oscillations

A pendulum is undergoing SHM with frequency f What is the frequency of its kinetic energy ?

$\frac{f}{2}$

2 f

3 f

4 f

Some More Questions From Oscillations Chapter

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin²(ωt) represents

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

The total energy of particle, executing simple harmonic motion is

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For Daily Free Study Material Join wiredfaculty

Oscillations

A pendulum is undergoing SHM with frequency f What is the frequency of its kinetic energy ? f2 2 f 3 f 4 f

Some More Questions From Oscillations Chapter

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin2(ωt) represents

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

The total energy of particle, executing simple harmonic motion is

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A pendulum is undergoing SHM with frequency f What is the frequency of its kinetic energy ?

$\frac{f}{2}$

2 f

3 f

4 f

The function sin²(ωt) represents