A) \[1:1\]
B) \[2:1\]
C) \[1:3\]
D) \[\sqrt{3}:1\]
Correct Answer: B
Solution :
\[{{y}_{1}}=5[\sin 2\pi t+\sqrt{3}\cos 2\pi t]\] \[=10\left[ \frac{1}{2}\sin \,2\pi t+\frac{\sqrt{3}}{2}\cos 2\pi t \right]\] \[=10\left[ \cos \,\frac{\pi }{3}\sin \,2\pi t+\sin \frac{\pi }{3}\cos \,2\pi t \right]\] \[=10\,\left[ \sin \left( 2\pi t+\frac{\pi }{3} \right) \right]\] \[\Rightarrow \] \[{{A}_{1}}=10\] Similarly, \[{{y}_{2}}=5\sin \left( 2\pi +\frac{\pi }{4} \right)\] \[\Rightarrow \] \[{{A}_{2}}=5\] Hence, \[\frac{{{A}_{1}}}{{{A}_{2}}}=\frac{15}{5}=\frac{2}{1}\]
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