A) \[5cm,\frac{3}{2}s\]
B) \[10cm,\frac{2}{3}s\]
C) \[5cm,\frac{2}{3}s\]
D) \[10cm,\frac{3}{2}s\]
Correct Answer: B
Solution :
The given equation is y = 5 \[(sin3\pi t+\sqrt{3}cos3\pi t)\] \[\Rightarrow \]\[y=2\times 5\left( \frac{1}{2}\sin 3\pi t+\frac{\sqrt{3}}{2}\cos 3\pi t \right)\] \[=10\left( \cos \frac{\pi }{3}\sin 3\pi t+\sin \frac{\pi }{3}\cos 3\pi t \right)\] \[y=10\sin \left( 3\pi t+\frac{\pi }{3} \right)\] ?.(i) Comparing eqn. (i) with standard equation \[y=A\sin (\omega t+\phi )\] \[\Rightarrow \]\[\omega =3\pi \]and \[A=10cm\] \[\therefore \]Time period \[T=\frac{2\pi }{\omega }=\frac{2}{3}s\]
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