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

Moderate

A

8
B

-4
C

4
D

$4 \sqrt{2}$

Solution

$x = 4 (\cos πt + \sin πt)$
= $4 \sqrt{2} [\frac{1}{\sqrt{2}} \cos πt + \frac{1}{\sqrt{2}} \sin πt]$
= $4 \sqrt{2} [\sin \frac{π}{4} cosπt + \cos \frac{π}{4} sinπt]$
$= 4 \sqrt{2} \sin (πt + \frac{π}{4})$
Standard equation of displacement is:
$x = a \sin (ωt + \emptyset)$
Comparing the given equation with standard equation
a = 4 $\sqrt{2}$

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