Question

The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 see respectively. If the initial phase is r/2 radiam,then the equaction of S.H.H. will be

• A. y = 0.5 sin$5/\pi$
• B. y = 0.5 sin$4/\pi$
• C. y = 0.5 sin$2.5/\pi$
• D. y = 0.5 cos$5\pi t$

Answer 1

The correct option is D y = 0.5 cos$5\pi t$

$\begin{array}{c}y=a\sin \left(\omega t+\phi \right)\\ =a\sin \left(\frac{2\pi }{T}t+\phi \right)\\ y=0.5\sin \left(\frac{2\pi }{0.4}t+\frac{\pi }{2}\right)\\ y=0.5\sin \left(5\pi t+\frac{\pi }{2}\right)\\ =0.5\cos 5\pi t\end{array}$