Simple harmonic motion diff. equation

[Breedlove]

Homework Statement

A mass of 1 slug is suspended from a spring whose spring constant is 9 lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of \sqrt{3} ft/s. Find the times at which the mass is heading downward at a velocity of 3 ft/s.

Homework Equations

x(double prime) + k/m x=0
(k/m)^(1/2)=w

The Attempt at a Solution

So first, m=1, k=9 and the initial conditions: x(0)=-1 and x(prime)(0)=-\sqrt{3}
x(double prime)+9x=0 which has roots (plus or minus)3i. The solution then looks like

x(t)=C1cos(3t)+C2sin(3t) and then plugging in initial conditions I get C1=-1, C2=-\sqrt{3}/3

Then converting it to another form where A=\sqrt{C1^2+C2^2} and phi=arctan(C1/C2)
x=Asin(wt+phi)
x=2\sqrt{3}/3 sin(3t+4pi/3)
Taking the derivative to get the velocity:
x(prime)=6\sqrt{3}cos(3t+4pi/3)
setting x(prime)=3 and solving for t yields a negative value for t, t=-.97

I know I didn't really show a lot of work in a form that is easy to read or understand, but where am I going wrong here? Thanks for any help you can provide!

 

[clamtrox]

Cosine function gets a given value in more than one point; maybe you should solve the first positive value of t where it holds.