Phase Constant

GatorJ

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_mcos(ωt + φ)? The vertical axis scale is set by vs = 7.50 cm/s.


2. Relevant equations
x = x_mcos(ωt + φ)
v=-ωx_msin(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_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