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What does f_0 mean?

  1. Dec 18, 2013 #1
    I found this equation for driven oscillators, and am unsure what the F_0 means, and how it's used. Can someone please briefly explain this?
    Also, I don't get what the difference is between the initial and final omega. (how can there be a final omega if it's constantly increasing?!?!?)
     

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  3. Dec 18, 2013 #2

    jhae2.718

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    ##F_0## is the amplitude of a sinusoidal forcing function, ##\omega_0## is the undamped natural frequency of the system, and ##\omega## is the frequency of the forcing function, which looks something like ##f(t)=f_0\sin(\omega t)## or ##f(t)=f_0\cos(\omega t)##.

    The definition of ##\omega## shown is also the damped natural frequency of the system.
     
    Last edited: Dec 18, 2013
  4. Dec 18, 2013 #3
    So are the units for F_0 meters? (So it's not a force?)
    Thanks.
     
  5. Dec 18, 2013 #4

    jhae2.718

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    ##F_0## has dimensions of force. You can easily see this by looking at the dimension of each part of the expression. Consider [tex]f(t)=f_0 \cos(\omega t).[/tex] The dimension of ##t## is of course time, and the dimension of ##\omega## must be angle/time so that ##\omega t## has dimensions of an angle (e.g. radians). This must be so, as, for example, what is the cosine of a second? It's meaningless. Since ##f(t)## is a force, and ##\cos(\omega t)## is dimensionless, it must be that ##f_0## has the dimensions of force, e.g. newtons for SI.
     
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