hit a bit of a wall with this one... I know the answer is right behind it!

Problem:

In a spring test, Eddie releases the spring from rest at a height of 20 cm beyond the spring's natural length (i.e. y(0)=20). He finds that the resulting vibration has a period of 1 s and that the amplitude of the vibration halves after 3 s ("half-life"). From his knowledge of damped springs, he also knows that the spring should behave according to the equation $y(t) = Ae^{-bt}cos(ct)$

Question:

Solve the function paramaters A, b and c

I've solved A = 20 by setting time = 0

And as the period = 1s then C must = 2pi (at least I believe)

just having trouble finding B. I know I have to set the function to half (y(t)/2) however that still leaves me with an unknown answer and an unknown variable.

Any help is much appreciated!