First slide

Simple hormonic motion

Question

Two simple harmonic motions are represented by
$y_{1} = 5 (\sin 2 πt + \sqrt{3} \cos 2 πt) y_{2} = 5 \sin (2 πt + \frac{π}{4})$
The ratio of the amplitude of two SHM's is:

Moderate

A

1 :1
B

1 : 2
C

2 :1
D

$1 : \sqrt{3}$

Solution

$y_{1} = 5 \times 2 (\frac{1}{2} \sin 2 πt + \frac{\sqrt{3}}{2} \cos 2 πt) = 10 (\sin 2 πt \cos \frac{π}{3} + \cos 2 πt \sin \frac{π}{3}) y_{1} = 10 \sin (2 πt + \frac{π}{3}) y_{2} = 5 \sin (2 πt + \frac{π}{4}) \Rightarrow \frac{A_{1}}{A_{2}} = \frac{10}{5} = \frac{2}{1}$

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