First slide

Simple hormonic motion

Question

The displacement of a particle varies according to the relation $x = 4 (\cos â¡ Ït + \sin â¡ Ït)$ The amplitude of the particle is

Moderate

A

8
B

4
C

-4
D

4 $\sqrt{2}$

Solution

Given x $x = 4 \cos â¡ Ït + 4 \sin â¡ Ït$
The equation of simple harmonic motion can be expressed as
$x = a_{1} \cos â¡ Ït + a_{2} \sin â¡ Ït a = \sqrt{(a_{1}^{2} + a_{2}^{2})} = \sqrt{(16 + 16)} = 4 \sqrt{2}$

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