Question

A simple motion is represented by:
$y=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)cm$
The amplitude and time period of the motion are:

• A. $5cm,\frac{3}{2}s$
• B. $5cm,\frac{2}{3}s$
• C. $10cm,\frac{3}{2}s$
• D. $10cm,\frac{2}{3}s$

Answer 1

The correct option is D $10cm,\frac{2}{3}s$

$y=5\left[\sin \right(3\pi t)+\sqrt{3}\cos (3\pi t\left)\right]$
$=10\sin (3\pi t+\frac{\pi }{3})$
Amplitude $=10cm$
$T=\frac{2\pi }{w}=\frac{2\pi }{3\pi }=\frac{2}{3}\sec$