First slide

Simple harmonic motion

Question

A S.H.M. is represented by $x = 5 \sqrt{2} (\sin 2 πt + \cos 2 πt) .$ The amplitude of the S.H.M. is

Moderate

A

10 cm
B

20 cm
C

$5 \sqrt{2} cm$
D

50 cm

Solution

$x = 5 \sqrt{2} (\sin 2 π t + \cos 2 π t)$
$= 5 \sqrt{2} \sin 2 π t + 5 \sqrt{2} \cos 2 π t$
$x = 5 \sqrt{2} \sin 2 πt + 5 \sqrt{2} \sin (2 π t + \frac{π}{2})$
Phase difference between constituent waves $φ = \frac{π}{2}$
$∴$ Resultant amplitude $A = \sqrt{{(5 \sqrt{2})}^{2} + {(5 \sqrt{2})}^{2}}$ =10 cm.

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