Solving for Phi in Harmonic Motion Equation

[lmf22]

A spring with spring constant 190 N/m vibrates with an amplitude of 8.0 cm when 0.380 kg hangs from it.
What is the equation describing this motion as a function of time?
Assume the mass passes through the equilibrium point, toward positive x (upward), at t = 0.100 s.

x=A*cos(omega*t + phi)

I figured out that A is 8.0 cm, and omega is 22.36
but I can't figure out phi.

Here's what I did:
x=0 (because it's at equalibrium at .100 s)
Plug in numbers and get
0=A*cos(22.36*.100 + phi)
0/A = cos(22.36*.100 + phi)
arcosine(0) = 22.36*.100 + phi
phi = arcosine(0) - (22.36*.100)

What am I doing wrong?

 

[NateTG]

There are many solutios for [itex]\phi[/tex]. Perhaps you're looking for a particular one? Perhaps you should use the fact that the mass is moving upwards at time [itex]t=0.100[/tex]?

 

[lmf22]

Ah! I got it! Thank you.