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10/01/2022 11:52 am
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Two simple harmonic motion, are represented by the equations y1 = 10 sin \(\Big( 3 \pi t + \frac{\pi}{3}\Big)\)
y2 = 5 (sin 3πt + √3 cos 3πt)
Ratio of amplitude of y1 to y2 = x : 1. The value of x is ________.
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10/01/2022 12:04 pm
y1 = 10 sin 10 sin \(\Big( 3 \pi t + \frac{\pi}{3}\Big)\)
⇒ Amplitude = 10
y2 = 5 (sin 3πt + √3 cos 3πt)
y2 = 10(\(\frac{1}{2}\) sin3πt + \(\frac{\sqrt 3}{2}cos3πt\))
y2 = 10(\(cos \frac{\pi}{3}\) sin3πt + \(sin\frac{\sqrt 3}{2}cos3πt\))
y2 = 10 sin\(\Big( 3 \pi t + \frac{\pi}{3}\Big)\) ⇒ Amplitude = 10
So ratio of amplitudes = \(\frac{10}{10}\) = 1