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Finding the phase constant

  1. Mar 20, 2017 #1
    1. The problem statement, all variables and given/known data
    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)

    2. Relevant equations
    x(t) = xmcos(ωt + Φ)
    v(t) = -ωxmsin(ωt + Φ)
    k = mω2

    3. 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?
     
  2. jcsd
  3. Mar 20, 2017 #2
    It looks like you may have 2 equations and 2 unknowns.

    Edit: Welcome to Physics Forums.
     
  4. Mar 20, 2017 #3

    haruspex

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