First slide

Simple hormonic motion

Question

Two simple harmonic motions given by $x_{1} = 3 \cos 10 t c m and x_{2} = 4 \sin 10 t c m$ are superposed on a particle. Then amplitude of motion of the particle is

Easy

A

7 cm
B

$5 \sqrt{2} c m$
C

$\sqrt{2} c m$
D

$5 c m$

Solution

$x_{1} = 3 \cos 10 t and x_{2} = 4 \cos (10 t - \frac{π}{2})$
$∴ A_{R} = \sqrt{3^{2} + 4^{2}} c m = 5 c m$

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