Finding Phase Constant for Harmonic Oscillator

AI Thread Summary
The discussion focuses on determining the phase constant for a harmonic oscillator based on a given velocity function. The position function is expressed as x = xmcos(ωt + φ), with the velocity function derived from it. An attempt to solve the problem yields a phase constant of -0.927 rad, which is incorrect as phase angles should be positive. A suggestion is made to convert the negative angle to a positive equivalent in the fourth quadrant, resulting in a phase constant of approximately 4.068 rad. The importance of correctly interpreting initial conditions in the context of the problem is emphasized.
GatorJ
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Homework Statement


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.
[PLAIN]http://img227.imageshack.us/img227/4729/qu1512.gif

Homework Equations


x = xmcos(ωt + φ)
v=-ωxmsin(ωt + φ)
vm=ωxm

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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Phase angle is always positive.
In this problem phase angle is in the fourth quadrant.
 
It is correct, but try to give in positive angle with the same sine: pi-phi= 4.068 rad.

ehild
 
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