harmonic oscillators

[photon_mass]

could someone please explain to me the phase angle? more specifically, what does it measure? i think it measures the initial displacement from the equilibrium position but i don't really get it.

[Chi Meson]

THis is a tricky concept, since there is no "angle" to phase angle.

Begin by thinking of any complete cycle as a circle. As a mass bobs up and down on a spring, think of one point of the cycle as being one point on a "reference circle." In one complete cycle of the oscillator, the point goes around one time on the circle. So every position of the oscillator has a "reference position" on a circle.

Obviously, you can describe the position on a circle by its angle. Phase angle is the position on this circle (usually in radians) for any part of the oscillation.

If you set the "radius" of the reference circle as the amplitude of the oscillator, then the math will translate the phase angle into the actual position of the oscillator.

[HallsofIvy]

Or think about a pendulum. We can, approximately, write the motion of the pendulum as θ= Θsin(t/T) if we take the θ to be 0 (pendulum hanging straight down at t=0, T the period, and Θ the amplitude of the motion. period and amplitude are characteristic of the motion, but when we decide to call t= 0 is our choice. You can show that different choices of when t= 0 is give θ= Θsin((t/T+ φ) where φ is the fraction of the motion that has been completed when t= 0- the "phase angle".

[photon_mass]

so it measures the initial displacement from the equilibrium position?

[Vector Sum]

so it measures the initial displacement from the equilibrium position?

The formula A cos wt gives you the displacement from equilibrium. the w (omega, really) is the phase angle.

[arildno]

Vector Sum:
w is the FREQUENCY, not the phase angle!!
This is easily argued from dimensional analysis:
w has dimension 1/(time unit), but angles are dimensionless..

[photon_mass]

ya, w is the angular frequency, not the phase angle.
i don't 100% understand what that means either. if someone could tell me what that is in 'normal' terms that would be much appreciated.these terms are confusing.
ok. i have thought up like, an example.
the distance between succesive maxima is:
A Cos[w t], A Cos[w t + 2 n pi]
where n is the number of maxima the maxima is away from the first maxima.
???
is phase angle phase difference? what is phase difference?
is that when there are multiple waves running at once? like the distance between maxima of the two waves?
these oscillators are driving me bonkers, and they aren't even damped or driven yet.
:grumpy:

[Vector Sum]

D'oh!

I knew that. My bad. And it was right in HallsofIvy's post.
Yes, phase angle is the "phi" after the wt, and it does give the "starting point" so to speak, of the oscillation. Phase difference is just that: the difference, in radians, between two angles. Could be the difference between two points for the same oscillator, or it could be the difference between two oscillators at the same time.

Heard of the term "180 degrees out of phase"?

[photon_mass]

yes. with electricity you have sine waves 180 degrees out of phase.
i think that's what makes AC.
thanks