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Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsOscillations3 Marks
Question
Two simple harmonic motions are represented by the following equations:$\text{y}_1=10\sin\frac{\pi}{4}(12\text{t}+1)$
and $\text{y}_2=5(\sin3\pi\text{t}+\sqrt{3}\cos\pi\text{t}).$ What is the ratio of their amplitudes?
✓

Answer

Here, $\text{y}_1=10\sin\frac{\pi}{4}(12\text{t}+1)$$=10\sin(3\pi\text{t}+\frac{\pi}{4}) \ ...(\text{i})$
and $\text{y}_2=5[\sin3\pi\text{t}+\sqrt{3}\cos3\pi\text{t}]$$=10\Big[\frac{1}{2}\sin3\pi\text{t}+\frac{\sqrt{3}}{2}\cos3\pi\text{t}\Big]$
$=10\Big[\cos\frac{\pi}{3}\sin3\pi\text{t}+\sin\frac{\pi}{3}\cos3\pi\text{t}\Big]$
$=10\sin\big(3\pi\text{t}+\frac{\pi}{3}\big) \ ...(\text{ii})$
Thus, from (i) and (ii), the amplitude ratio of motion $=\frac{10}{10}=\frac{1}{1}=1:1$

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