Question

The amplitude and the periodic time of a SHM are $5cm$ and $6s$ respectively. At a distance of $2.5cm$ away from the mean position, the phase will be

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{5\pi }{12}$

Answer 1

The correct option is C $\frac{\pi }{6}$

The equation of motion is given as
$y=5\sin \frac{2\pi t}{6}$
Here, $y=2.5cm$
$\therefore 2.5=5\sin \frac{2\pi t}{6}$
$\Rightarrow \frac{\pi }{6}=\frac{2\pi t}{6}\Rightarrow t=\frac{1}{2}s$
$\therefore$ The phase $=\frac{2\pi t}{6}=\frac{2\pi }{6}\times \frac{1}{2}=\frac{\pi }{6}$