The motion of a spring that is subject to a frictional force or a damping force (such as

Chapter 3, Problem 69

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

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