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Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsOscillations3 Marks
Question
Two simple harmonic motions are represented by:$\text{x}_1=10\sin\Big(4\pi\text{t}+\frac{\pi}{4}\Big)$
$\text{x}_2=5(\sin4\pi\text{t}+\sqrt{3}\cos4\pi\text{t})$
What is the ratio of the amplitudes?
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Answer

$\text{x}_2=5\sin4\pi\text{t}+5\sqrt{3}\cos4\pi\text{t}$Amplitude of $\text{x}_2=\sqrt{5^2+(5\sqrt{3})^2}=10$
Since the $\sin\pi\text{t}$ and $\cos4\pi\text{t}$ functions are out ofphase by $\frac{\pi}{2}.$
Amplitude of $x_2 = 10$
$\therefore$ Ratio of amplitudes is $1 : 1$

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