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Thread: amp, period, frequency, ps

  1. #1
    Jan 2006

    Cool amp, period, frequency, ps

    How can I find the period, frequency, and phase shift to problems set up like..

    h= -15cos (pie t/3) +21

    what if it is like

    E= 150cos 80 pie t

    I am familiar with solving these equations with. . 360/k and -c/k and all that, but this time around I'm not getting the right results. I thought maybe these problems were set up differently. I sometimes have trouble with working with radians. I don't think these are difficult, but i need to have the right approach. help would be great!
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  2. #2
    Global Moderator

    Nov 2005
    New York City
    A trigonometric function (sine cosine) has form
    $\displaystyle y=A\sin(Bx+C)+K$
    $\displaystyle y=A\cos(Bx+C)+K$
    where $\displaystyle A,B,C,D$ are real numbers.
    The coefficient $\displaystyle A$ is called the amplitude. It is half the distance between the highest point on the wave and the lowest point point on the wave. The coefficient $\displaystyle B$ is called the frequency. It shows the number of times the wave goes though complete cycles. The period is the number of radians which gives the full cycle it is determined by $\displaystyle \frac{2\pi}{|B|}$.
    Next, the coffiecient $\displaystyle C$ is called the phase shift, it shifts the wave to the left or right by that many radians. If $\displaystyle C>0$ the wave is shifted to the left, if $\displaystyle C<0$ the wave is shifted to the right.
    Finally, $\displaystyle K$ just determines the shift up or down for the wave. If $\displaystyle K>0$ the wave is moved up by that many units. If $\displaystyle K<0$ the wave is moved down by that many units. And if $\displaystyle K=0$ the wave is just left the way it is.

    Now you should be able to do your problems, if not say where you need help with.
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