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, then 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

Answer: (D)

$y = 0.5\cos 5\pi t$

Answer 2

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

$= a\sin\left( \frac{2\pi}{T}t + \varphi \right)$⇒$y = 0.5\sin\left( \frac{2\pi}{0.4}t + \frac{\pi}{2} \right)$

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