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Phase Constant

  1. Apr 2, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in Fig. 15-30 if the position function x(t) has the form x = xmcos(ωt + φ)? The vertical axis scale is set by vs = 7.50 cm/s.
    [​IMG]

    2. Relevant equations
    x = xmcos(ωt + φ)
    v=-ωxmsin(ωt + φ)
    vm=ωxm

    3. The attempt at a solution

    From graph, vm=9.375 cm/s

    vm=9.375 cm/s = ωxm

    xm=9.375/ω

    At t=0, v(0)=7.5 cm/s=-ωxmsin(φ)

    φ=sin-1(7.5/-ωxm)

    φ=sin-1(7.5/-ω*9.375/ω)

    φ=sin-1(7.5/-9.375)= -.927 rad

    I still got it wrong and not sure where I messed up. Only thing that I can think of is that I incorrectly assumed t=0 is 7.5 cm/s and if that's the case then I don't know where to begin on this problem.
     
  2. jcsd
  3. Apr 2, 2010 #2

    rl.bhat

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    Homework Helper

    Phase angle is always positive.
    In this problem phase angle is in the fourth quadrant.
     
  4. Apr 2, 2010 #3

    ehild

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    Homework Helper
    Gold Member

    It is correct, but try to give in positive angle with the same sine: pi-phi= 4.068 rad.

    ehild
     
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