# Phase Constant

## 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 [Broken]

## 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)

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.

Last edited by a moderator:

rl.bhat
Homework Helper
Phase angle is always positive.
In this problem phase angle is in the fourth quadrant.

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

ehild

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