Finding the Phase Constant in a Mass/Spring System

[emilli]

Homework Statement

A mass/spring system is set in motion. Find the phase constant with the given information.

Given:
k = 8 N/m (spring constant)
m = 0.1 kg (mass attached to string)
x₀ = -0.12 m (position at t = 0)
v₀ = 0.9 (velocity at t = 0)

Homework Equations

x(t) = x_mcos(ωt + Φ)
v(t) = -ωx_msin(ωt + Φ)
k = mω²

The Attempt at a Solution

I first solved for ω using the given spring constant and mass: ω = √(k / m) = √(8N/m / 0.1kg) = 8.94 rad/s
At t = 0,
x(0) = x_mcos(Φ)
v(0) = -ωx_msin(Φ)
Unfortunately, this was where I became stumped. I don't know how to find the amplitude(x_m) which is the only thing I needed to solve for the phase constant. Any hints to what I should do?

 

[TomHart]

It looks like you may have 2 equations and 2 unknowns.

Edit: Welcome to Physics Forums.

 

[haruspex]

how to find the amplitude(xm)

You don't need to find it, you need to eliminate it.