Answer
$s(t) = 2~e^{-1.5t}~sin~2\pi t$
$v(t) = e^{-1.5t}\cdot (-3~sin~2\pi t+4\pi~cos~2\pi t)$
We can see a sketch of the graphs below.
Work Step by Step
$s(t) = 2~e^{-1.5t}~sin~2\pi t$
We can find $v(t)$:
$v(t) = s'(t) = (-1.5)(2~e^{-1.5t}~sin~2\pi t)+(2\pi)(2~e^{-1.5t}~cos~2\pi t)$
$v(t) = e^{-1.5t}\cdot (-3~sin~2\pi t+4\pi~cos~2\pi t)$
We can see a sketch of the graphs below.
