The displacement of a particle along the x -axis is given by x=a ^2 ω t . The motion of the particle corresponds to

Correct answer: C. non simple harmonic motion Given, X=asin^2 ω t or X=a ((1- 2 ω t)/(2)) [ 2 θ=1-2 ^2 θ] or X=(a)/(2)-(a 2 ω t)/(2) Now, V=(d x)/(d t)=a ω 2 ω t and a=d v / d t=2 a ω^2 2 ω t Here, a is not directly proportional to (-x) which is a condition for SHM.

JIPMER 2017

Exam: JIPMER
Year: 2017
Subject: Physics
Chapter: Oscillations

JIPMER 2017 · Physics · Oscillations

The displacement of a particle along the x -axis is given by x=a ^2...

The displacement of a particle along the

x

-axis is given by

x=a \sin ^2 \omega t

. The motion of the particle corresponds to

Options

Asimple harmonic motion of frequency $\omega / \pi$
Bsimple harmonic motion of frequency $3 \omega / 2 \pi$
Cnon simple harmonic motion
Dsimple harmonic motion of frequency $\omega / 2 \pi$

Correct answer

C. non simple harmonic motion

Step-by-step solution

Given,

X=\operatorname{asin}^2 \omega t

X=a

\left(\frac{1-\cos 2 \omega t}{2}\right) \quad

\left[\because \cos 2 \theta=1-2 \sin ^2 \theta\right]

X=\frac{a}{2}-\frac{a \cos 2 \omega t}{2}

Now,

V=\frac{d x}{d t}=a \omega \sin 2 \omega t

and

a=d v / d t=2 a \omega^2 \cos 2 \omega t

Here,

a

is not directly proportional to

(-x)

which is a condition for SHM.

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