First slide

Simple hormonic motion

Question

Acceleration (a) vs displacement (x) graph of a particle executing simple harmonic motion along a straight line is shown in the diagram. Then frequency of oscillation is

Moderate

A

$\frac{4}{π} Hz$
B

$\frac{2}{π} Hz$
C

$\frac{1}{π} Hz$
D

$\frac{1}{2 π} Hz$

Solution

Acceleration is given by, $a = - ω^{2} x$
From the graph, $- ω^{2} = \tan (180^{o} - 45^{o}) \Rightarrow ω^{2} = \tan 45^{o} \Rightarrow ω = 1 rad / s$
$∴ f = \frac{ω}{2 π} = \frac{1}{2 π} Hz .$

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