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Chapter 3.3, Problem 65E

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 ) = 2 e 1.5 t sin 2 π t

where s is measured in centimeters and t in seconds. Find the velocity after t seconds and graph both the position and velocity functions for 0 t 2 .

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