Question 261: Oscillations

Question

The kinetic energy of a particle, executing simple harmonic motion is 16 J when it is in mean position. If amplitude of motion is 25 cm and the mass of the particle is 5.12 kg , the period of oscillation is

Accepted Answer

Given:
Kinetic Energy (K.E.) at mean position = 16 J
Amplitude (A) = 25 cm = 0.25 m
Mass (m) = 5.12 kg
The kinetic energy at the mean position is equal to the total energy of the particle in simple harmonic motion. Therefore, we have:
Total energy $ E = \frac{1}{2} m \omega^2 A^2 = 16 $
To find the angular frequency $\omega$, we rearrange the equation:
$ \omega^2 = \frac{16 	imes 2}{5.12 	imes (0.25)^2} = 10^2 $
Thus, the angular frequency is:
$ \omega = 10 $
The period $ T $ of oscillation is given by:
$ T = \frac{2 \pi}{\omega} = \frac{2 \pi}{10} = \frac{\pi}{5} \, 	ext{s} $

Answer

$\frac{\pi}{5} \mathrm{~s}$

Answer

$2 \pi \mathrm{~s}$

Answer

$20 \pi \mathrm{~s}$

Answer

$5 \pi \mathrm{~s}$

Oscillations

The kinetic energy of a particle, executing simple harmonic motion is 16 J when it is in mean position. If amplitude of motion is 25 cm and the mass of the particle is 5.12 kg , the period of oscillation is

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