MHT CET · Physics · Oscillations
Two simple harmonic motions are represented as \(y_1=10 \sin \omega t\) and \(y_2=10 \sin \omega t+5 \cos \omega t\). The ratio of the amplitudes of \(y_1\) and \(y_2\) is
- A \(1: \sqrt{2}\)
- B 1:4
- C 1:1
- D \(2: \sqrt{5}\)
Answer & Solution
Correct Answer
(D) \(2: \sqrt{5}\)
Step-by-step Solution
Detailed explanation
Given, \(Y_1=10 \sin \omega t\) and
\(Y_2=10 \sin \omega t+5 \cos \omega t\)
Amplitude of \(Y_1\) and \(A_1=10\)
Amplitude of \(Y_2\) is \(A_2=\sqrt{(10)^2+(5)^2}=5 \sqrt{5}\)
Thus, \(\frac{A_1}{A_2}=\frac{10}{5 \sqrt{5}}=2: \sqrt{5}\)
\(Y_2=10 \sin \omega t+5 \cos \omega t\)
Amplitude of \(Y_1\) and \(A_1=10\)
Amplitude of \(Y_2\) is \(A_2=\sqrt{(10)^2+(5)^2}=5 \sqrt{5}\)
Thus, \(\frac{A_1}{A_2}=\frac{10}{5 \sqrt{5}}=2: \sqrt{5}\)
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