Homework Help: Finding Phase Constant

1. Nov 12, 2009

1. The problem statement, all variables and given/known data
Part (a) of the figure below is a partial graph of the position function x(t) for a simple harmonic oscillator with an angular frequency of 1.35 rad/s; Part (b) of the figure is a partial graph of the corresponding velocity function v(t). The vertical axis scales are set by xs = 6.5 cm and vs = 7.0 cm/s. What is the phase constant of the SHM if the position function x(t) is given by the form x = xmcos(ωt + ϕ)?

2. Relevant equations
x = xmcos(ωt + ϕ)
v = -ωxmsin(ωt + ϕ)

3. The attempt at a solution

For the X vs. t graph the line crosses t=0 when x = 2.6. For the V vs. t graph the line crosses t=0 when v=-5.6.

I thought then I could just plug all the number in and find out when they are equal

2.6 = 6.5cos(1.35*0+ϕ)
-5.6 = -8.775sin(1.35*0+ϕ)

I subtracted 2.6 from both sides for the first equation and added 5.6 to both sides for the second. I then set them equal. I used my calculator to attempt to solve them.

Looking at them separately it looks like it should be 1.15 radians for X and .69 radians for V (Roughly).

I can't figure out what I'm doing wrong. Perhaps I shouldn't be reading the graph like I am. or I am simply reading it wrong.

2. Nov 12, 2009

Found an answer. I don't understand why this is correct, but dividing velocity by position gives the following

v/x = tan-1($$\frac{Velocity @ t=0}{Position @ t=0 TIMES Angular Frequency}$$)

So that leaves

tan-1($$\frac{-5.6}{2.6 * 1.35}$$) = -1.01

I think then since it is shifted I changed it to positive 1.01.

That answer was taken as correct.

3. Nov 12, 2009

regas99

One equation represents position and the other represents velocity. Since the units are different, you can never "set them equal."