Solving for Phi in Harmonic Motion Equation

AI Thread Summary
The discussion centers on determining the phase constant (phi) in the harmonic motion equation for a spring-mass system. The spring has a constant of 190 N/m and an amplitude of 8.0 cm, with a mass of 0.380 kg. The equation for motion is given as x=A*cos(omega*t + phi), with A identified as 8.0 cm and omega calculated to be 22.36. The user initially struggles to find phi by setting x to 0 at t=0.100 s but realizes that considering the direction of motion (upward) at that time is crucial. Ultimately, the correct approach involves recognizing that multiple solutions for phi exist, and the upward motion provides additional context for determining the specific solution needed.
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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?
 
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There are many solutios for \phi[/tex]. Perhaps you're looking for a particular one? Perhaps you should use the fact that the mass is moving upwards at time t=0.100[/tex]?
 
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Ah! I got it! Thank you.
 
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