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Phase Constant

by GatorJ
Tags: constant, phase
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GatorJ
#1
Apr2-10, 10:53 AM
P: 3
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.


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.
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rl.bhat
#2
Apr2-10, 11:15 AM
HW Helper
P: 4,433
Phase angle is always positive.
In this problem phase angle is in the fourth quadrant.
ehild
#3
Apr2-10, 11:20 AM
HW Helper
Thanks
P: 10,551
It is correct, but try to give in positive angle with the same sine: pi-phi= 4.068 rad.

ehild


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