First slide

Simple hormonic motion

Question

The displacement of a particle varies according to the relation. $x = 4 (\cos πt + \sin πt)$ The amplitude of the particle is:

Easy

A

-4
B

4
C

$4 \sqrt{2}$
D

8

Solution

$x = 4 (\cos πt + \sin πt) = 4 \sqrt{2} [\frac{1}{\sqrt{2}} cosπt + \frac{1}{\sqrt{2}} \sin πt] = 4 \sqrt{2} [\sin \frac{π}{4} \cos πt + \cos \frac{π}{4} \sin πt] = 4 \sqrt{2} \sin (πt + \frac{π}{4}) \Rightarrow Amplitude = 4 \sqrt{2}$

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