Finding Phase Constant for Harmonic Oscillator

[GatorJ]

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 = x_mcos(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 = x_mcos(ωt + φ)
v=-ωx_msin(ωt + φ)
v_m=ωx_m

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_msin(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.

 

[rl.bhat]

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

 

[ehild]

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

ehild