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 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 ≤ 1 ≤ 2.
To find: The velocity after t seconds.
The equation of motion of a point on such a spring is .
(1) Constant Multiple Rule:
(2) Product Rule:
If is a displacement of a particle and the time t is in seconds, then the velocity of the particle is .
Obtain the velocity at time t.
Apply the product rule (2) and the constant multiple rule (1),
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