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22. Two simple harmonic motions are represented by the equations \( y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{4}\right) \) and \( y_{2}=5(3 \sin 3 \pi t+\sqrt{3} \cos 3 \pi t) \). Their amplitudes are in the ratio ofa. \( \sqrt{3} \)b. \( 1 / \sqrt{3} \)C. 2d. \( 1 / 6 \) |
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Answer» Given, y1 = 10 sin (3πt + \(\frac{\pi}{4}\)) y2 = 5 (3 sin3πt + \(\sqrt 3\) cos3πt) y2 = 15 sin3πt + \(5\sqrt 3\) cos3πt Amplitude of y1 is A1 = 10 Amplitude of y2 is A2 = \(\sqrt{(15)^2+(5\sqrt3)^2}\) A2 = \(\sqrt{225+(8.6)^2}\) A2 = \(\sqrt{225+73.96}\) A2 = \(\sqrt{298.96}\) A2 = 17.29 Then ratio of amplitude is : \(\frac{A_1}{A_2}\) = \(\frac{10}{17.29}\) \(\frac{A_1}{A_2}\) = \(\frac{1}{\sqrt 3}\) Hence, Option (b) is correct. |
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