(adsbygoogle = window.adsbygoogle || []).push({}); 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 = x_{m}cos(ωt + φ)? The vertical axis scale is set by vs = 7.50 cm/s.

2. Relevant equations

x = x_{m}cos(ωt + φ)

v=-ωx_{m}sin(ωt + φ)

v_{m}=ωx_{m}

3. The attempt at a solution

From graph, v_{m}=9.375 cm/s

v_{m}=9.375 cm/s = ωx_{m}

x_{m}=9.375/ω

At t=0, v(0)=7.5 cm/s=-ωx_{m}sin(φ)

φ=sin^{-1}(7.5/-ωx_{m})

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.

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# Phase Constant

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