A) 1 : 2
B) 2 : 1
C) 1 : 1
D) None of these
Correct Answer: C
Solution :
\[{{y}_{1}}=10\sin \,\left( 3\pi t+\frac{\pi }{3} \right)\] ...(i) and \[{{y}_{2}}=5[\sin 3\pi t+\sqrt{3}\cos \,3\pi t]\] \[=5\times 2\,\left[ \frac{1}{2}\times \sin 3\pi t+\frac{\sqrt{3}}{2}\times \cos 3\pi t \right]\] \[=10\,\left[ \cos \frac{\pi }{3}\sin 3\pi t+\sin \frac{\pi }{3}\cos \pi t \right]\] \[=10\,\left[ \sin \,\left( 3\pi t+\frac{\pi }{t} \right) \right]\] ... (ii) (\[\because \] sin(A + B) = sinA cosB + cosA sinB) Comparing equation (i) and (ii) we get ratio of amplitude 1 : 1.
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