Answer
(a) greater than $0.50m/s$
(b) $0.79m/s$
(c) $1.2J$
Work Step by Step
(a) We can see from the figure that the speed is less than $2\pi$, hence the angular speed is greater than $1~rad/s$ and thus the maximum speed is greater than $0.50m/s.$
(b) We can find the maximum speed as follows:
$\omega=\frac{2\pi}{T}$
$\omega=\frac{\pi}{2}(4.0)=\frac{\pi}{2}s^{-1}$
Now $v_{max}=A\omega$
We plug in the known values to obtain:
$v_{max}=(0.5)(\frac{\pi}{2})=0.79m/s$
(c) The required energy can be determined as:
$E=\frac{1}{2}mv_{max}^2$
We plug in the known values to obtain:
$E=\frac{1}{2}(3.8)(0.785)^2$
$E=1.2J$
