displacement (s) of a spring is given as s=ae^(-kt)sin2pi*f*t where t is time.

Question

determine velocity and acceleration affter 2seconds if: a=3, k=0.75 and f=20.

i think im supposed to integrate but cant think how to do this one.

Answer 1

s = ae^-kt sin 2πft
s' = -ak e^-kt sin 2πft + ae^-kt (2πf) cos 2πft
= ae^-kt (-ksin 2πft + 2πf cos 2πft)

s" = -ake^-kt (-ksin 2πft + 2πf cos 2πft) + ae^-kt (-2πkf sin 2πft - 4π^2f^2 sin 2πft)

I'll let you check my algebra and plug in the values.