Find the time constant of a damped system

[hamsterB]

Homework Statement

A 3.9kg block hangs from a spring with constant 2160 N/m. The block is pulled down 6.2 cm from the equilibrium position and given an initial velocity of 1.5 m/s back towards equilibrium. The mass and spring are now immersed in water to damp the motion, so that the amplitude is reduced to 5% of its original value in 25 seconds. What is the time constant?

Homework Equations

τ=m/b where b is damping constant
xmax(t)=Ae^-t/2τ

The Attempt at a Solution

In previous parts of the question I found that the Amplitude (before damping) is 89cm, but I'm not sure if that's useful in this problem. I thought there might be some way to find out what the damping constant is from the fact that it reduces to 5% of A in 25 seconds, and then just plug that into τ=m/b, but I'm not sure how to go about that. Any help would be really appreciated!

 

[Simon Bridge]

I thought there might be some way to find out what the damping constant is from the fact that it reduces to 5% of A in 25 seconds,...

Sounds good to me - what does the equation of damped harmonic motion look like?