# Calculus

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The motion of a spring that is subject to dampening (such as a car's shock absorber)is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion for a point on such a spring is

s(t)=3∗e^(−2t)sin(3ðt)
where t is given in seconds.

a. Find the velocity of the point after t seconds.
v = .

b. Graph the velocity function and find the first time the velocity is 0.
t =

• Calculus -

for velocity, just take the derivative:

v(t) = -3e^(-2t) (2sin 3πt - 3πcos 3πt)

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