Simple Harmonic Motion Ques 52
- Two simple harmonic motions are represented by the equations $\quad y _1=10 \sin (3 \pi t+\pi / 4) \quad$ and $y _2=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$. Their amplitudes are in the ratio of …… .
$(1986,2 M)$
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Answer:
Correct Answer: 52.$1: 1$
Solution:
Formula:
- $A _1=10$ (directly)
For $A _2: y _2=5 \sin 3 \pi t+5 \sqrt{3} \cos 3 \pi t$
$ =5 \sin 3 \pi t+5 \sqrt{3} \sin 3 (\pi t+\frac{\pi}{2}) $
i.e. phase difference between two functions is $\frac{\pi}{2}$, so the resultant amplitude $A _2$ can be obtained by the vector method as under
$ A _2 =\sqrt{(5)^{2}+(5 \sqrt{3})^{2}}=10 $
$\therefore \quad \frac{A _1}{A _2} =\frac{10}{10}=1$
BETA
