First slide

Simple harmonic motion

Question

The variation of potential energy of harmonic oscillator is as shown in figure. The spring constant is

Moderate

A

$1 \times 10^{2} N / m$
B

150 N/m
C

$0 .667 \times 10^{2} N / m$
D

$3 \times 10^{2} N / m$

Solution

Total potential energy = 0.04 J
Resting potential energy =0.01 J
Maximum kinetic energy =(0.04–0.01)
$= 0 .03 J = \frac{1}{2} m ω^{2} a^{2} = \frac{1}{2} {ka}^{2}$
$0 .03 = \frac{1}{2} \times k \times {(\frac{20}{1000})}^{2}$
$k = 0 .06 \times 2500 N / m = 150 N / m$

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