Question : what is the phase angle

Hi

I dont understand what the phase angle of a sinusoidal function is. The book I am reading has defined a function that shows sinusoidal variation as

x = A sin(2pi * t/T) where A = amplitude and T = period of wave and t = time
x = A sin(omega * t) where omega = 2*pi*f and f=1/T

This equation was built up by describing the motion of a pendulum with amplitude A and period = T

The description of the phase angle which i don't follow is:

"We chose to start the clock then the pendulum reached the middle of the oscillation. How would we describe the oscillation if someone else controlled the clock and t=0 was some other time. (I'm ok to here). The easiest way to deal with this is the note the time at which the pendulum passes the midpoint, call it to, and substract this value from all times (????). We now describe the oscillation as

x = A sin(omega * (t-to))

We then invent a phase angle (i cant tell what symbol it is so i'll call it pa) pa = - omega * to and write
x= A sin(omega*t + pa)

I don't know what it means and thats all the explanation there is. I've attached a picture from the book

thanks

Attachments:

pend.jpg (22 KB)  (File Type Details) 

pendulum

Answer : what is the phase angle

The paragraph you quoted sounds like they're trying to 'express it in common language' which sometimes means vague.  If you look at http://www.answers.com/topic/phase-angle-measurement ,  you'll see a picture of two sine waves offset from each other.  The difference in time is the phase angle difference between the two.  Phase angle has to refer to some reference.  't0' is one possibility, another wave is the other choice.