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?✓
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 x2 = 10
$\therefore$ Ratio of amplitudes is 1 : 1
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