Solving Spring Homework: Angular Frequency & Amplitude

[XJellieBX]

Homework Statement

A block on a spring is pulled to the right and released at t=0s. It passes x=3.00cm at t=0.685s, and it passes x=-3.00cm at t=0.886s.
a) What is the angular frequency?
b) What is the amplitude?

Homework Equations

x(t)=Acos(wt+phi_0)

The Attempt at a Solution

Since the spring was initially pulled to the right, I assumed that the distance it was pulled would be the amplitude and with the initial conditions x₀=Acos(phi_0)=A, I set phi_0=0. Plugging in the times and positions,
x(t=0.685s)=Acos(0.685w)
x(t=0.886s)=Acos(0.886w).
I tried solving for an equation for A and plugging it into the other equation, but it just ended up looking like a complicated mess. Any insight would be appreciated =)

 

[LowlyPion]

There might be some insight to be gained by observing that the times given are for equal but opposite displacements about 0. Presumably the block and spring are at rest at x = 0.

 

[Jacobpm64]

or you have

two equations
3.00=Acos(0.685w) and
-3.00=Acos(0.886w).

I would divide the equations, then A cancels, and you might have an easier time solving for w.