The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is
S(t) = 2e-1.5t sin 2πt
where is measured in centimeters and in seconds. Find the velocity after seconds and graph both the position and velocity functions for 0 ≤ t ≤ 2.