Question

The amplitude and the time period in a S.H.M. is 0.5 cm and 0.4 sec respectively. If the initial phase is $\pi$/2 radian, than the equation of S.H.M. will be

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

Answer 1

The correct option is A y =0.5 sin 5$\pi$t

The equation of SHM is given by:

$y=a\sin (\omega t+\varphi )$

$=a\sin (\frac{2\pi }{T}t+\varphi )$

$\Rightarrow y=0.5\sin (\frac{2\pi }{0.4}t+\frac{\pi }{2})$

$y=0.5\sin (5\pi t+\frac{\pi }{2})=0.5\cos 5\pi t$