Maximizing Mass Motion with Minimal Hand Movement

[wolves5]

A student gets a 3 kg mass to oscillate up and down on bottom of a light vertical spring by pulling her hand up and down on the top end of the spring. The spring is a real spring with a spring constant of 94 N/m and a damping constant of 0.6 N sec/m.

(a) At what approximate frequency should the student move her hand up and down to get the maximum motion from the mass with the minimum motion of her hand?

The frequency I got was 0.890886 and its correct. I did 2pi times (sq.rt 3/94) and got 1.12247. To get frequency, I did 1/1.12247 and got 0.890886 seconds.

(b) The student now stops moving her hand and the mass slowly comes to rest. How long after she stop shaking her hand will it take for the amplitude of the mass to reach one half its maximum amplitude?

I don't know how to start this.

 

[ideasrule]

Do you know the equation of motion for the mass? If not, I'm pretty sure your physics textbook solves for it somewhere, so try looking for that.