Question

Derivative word problem:


The motion of a spring that is subject to a frictional force or a dampening 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) = 3e^(-4.5t)sin (2πt), where s is measured in centimeters and t in seconds. Find the velocity after t seconds.

Answer 1

derivative of fg = g'f + gf'.
so if, f = 3e^(-4.5t) and g = sin(2πt)
then...
the derivative of f = 3e^(-4.5t)
the derivative of g = cos(2πt)
plug in respectively...
s'(t) = (cos(2πt) * 3e^(-4.5t)) + (sin(2πt) * 3e^(-4.5t))

s'(t) = 3e^(-4.5t) * (cos(2πt) + sin(2πt))

The above should be your velocity, please correct me if I'm wrong.

Answer 2

Great! Thanks!

Answer 3

You're welcome