Phase Constant

  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. rl.bhat

    rl.bhat 4,435
    Homework Helper

    Chegg
    Phase angle is always positive.
    In this problem phase angle is in the fourth quadrant.
     
  4. ehild

    ehild 12,278
    Homework Helper
    Gold Member
    2014 Award

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

    ehild
     
    Curieuse likes this.
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