The ratio of amplitudes of two simple harmonic motions represented by the equations $y_{1} = 5 sin (\begin{matrix} 2 π t + \frac{π}{4} \end{matrix})$ and $y_{2} = 2 \sqrt{2} (sin 2 π t + cos 1 π t)$ is

1 : 1

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2 : 1

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5 : 2

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5 : 4

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2 : 5

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Solution

The correct option is D 5 : 4
The amplitude for first SHM equation, $A_{1} = \sqrt{5^{2}} = 5$ and
the amplitude for second SHM equation, $A_{2} = \sqrt{(2 \sqrt{2})^{2} + (2 \sqrt{2})^{2}} = \sqrt{8 + 8} = \sqrt{16} = 4$
Thus, $\frac{A_{1}}{A_{2}} = \frac{5}{4}$

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Similar questions

Y_{1} = 10 sin (3 π t + \frac{π}{4})

Y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)

y_{1} = 10 sin (3 π t + π / 4)

y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)

y_{1} = 5 (sin 2 π t + \sqrt{3} cos 2 π t)

y_{2} = 5 (sin 2 π t + \frac{π}{4})

y_{1} = 10 s i n \frac{π}{4} (12 t + I), y_{2} = 5 (s i n 3 p t + \sqrt{3} c o s 3 p t)

y_{1} = 10 sin \frac{π}{4} (12 t + 1), y_{2} = 5 (((sin 3 p t + \sqrt{3} cos 3 p t)

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