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COE in SHM

Two harmonic ...

Question

Two harmonic motions are represented by the equations $y_{1} = 10 s i n (3 π t + \frac{π}{4}), y_{2} = 5 (s i n 3 π t + \sqrt{3} s i n 3 π t)$ . Then their Amplitudes are in the ratio of

A

2:1

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B

1:2

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C

1:1

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D

4:1

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Solution

The correct option is C 1:1
$A_{1} = 10$ and $A_{2} = {[5^{2} + (5 \sqrt{3})^{2}]}^{1 / 2} = 10$

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