First slide

Simple hormonic motion

Question

The frequency of oscillation $(\frac{10}{π})$ (in Hz) of a particle of mass 0.1 kg which executes SHM along x-axis. The kinetic energy is 0.3 J and potential energy is 0.2J at position x = 0.02 m. The potential energy is zero at mean position. Find the amplitude of oscillations (in meters)

Moderate

A

$\frac{1}{2 \sqrt{10}}$
B

$\frac{1}{\sqrt{10}}$
C

$\sqrt{10}$
D

$2 \sqrt{10}$

Solution

$E_{t o t a l} = \frac{m ω^{2} A^{2}}{2} 0.5 = \frac{0.1 \times 4 \times π^{2}}{2} \times \frac{100}{π^{2}} \times A^{2} S o A = \frac{1}{2 \sqrt{10}} m$

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