Answer
Amplitude=2
Period$=\pi$ sec
frequency$=\frac{1}{\pi}$ rotations per sec
Work Step by Step
Since the particle moves uniformly around a circle of radius $2$ units, its amplitude $a$ is $2$. Also, it is given that the angular speed $w$ is 2 cycles per second. As we are interested in the displacement $s(t)$ of the particle from the equilibrium position, the equation is:
$s(t)=a\sin wt$
$s(t)=2\sin 2t$
We know that the amplitude is 2. In addition, $w$ can be used to find the period:
Period$=\frac{2\pi}{w}$
Period$=\frac{2\pi}{2}$
Period$=\pi$ sec
Since frequency is the reciprocal of period, frequency$=\frac{1}{\pi}$ rotations per sec
