First slide

Simple harmonic motion

Question

A particle executes SHM along x-axis with a frequency $(\frac{25}{π}) Hz$ . The mass of the particle is 0.20 kg. At the position x = 0.04 m, the kinetic energy is 0.50 J and the potential energy is 0.40 J. The potential energy is zero at mean position. The amplitude of oscillations (in cm) is __________.

Moderate

Solution

$K = (2 π f)^{2} m$
Energy of oscillations = 0.9 J
$\begin{array}{l} 0.90 = \frac{1}{2} K A^{2} \\ A = {[\frac{1.8}{4 π^{2} f^{2} m}]}^{1 / 2} = \frac{1}{2 π f} {[\frac{1.8}{0.2}]}^{1 / 2} = 6 cm \end{array}$

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