Finding the Phase Constant in a Mass/Spring System

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To find the phase constant in a mass/spring system, the angular frequency ω is calculated using the formula ω = √(k/m), resulting in 8.94 rad/s. The position and velocity equations at t = 0 are set up as x(0) = xmcos(Φ) and v(0) = -ωxmsin(Φ). The key to solving for the phase constant Φ is to eliminate the amplitude xm rather than finding its value directly. By manipulating these equations, one can derive a relationship that allows for solving Φ without needing xm. This approach simplifies the problem and leads to the correct determination of the phase constant.
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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) = xmcos(ωt + Φ)
v(t) = -ωxmsin(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) = xmcos(Φ)
v(0) = -ωxmsin(Φ)
Unfortunately, this was where I became stumped. I don't know how to find the amplitude(xm) which is the only thing I needed to solve for the phase constant. Any hints to what I should do?
 
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It looks like you may have 2 equations and 2 unknowns.

Edit: Welcome to Physics Forums.
 
emilli said:
how to find the amplitude(xm)
You don't need to find it, you need to eliminate it.
 
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