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What does sec^-1 mean?

  1. Feb 21, 2004 #1
    I've got a problem where I'm given some variables that I don't understand the value of. The formula is for horizontal displacement of damped oscillating objects. The values I'm not understanding are:

    (beta) = 0.1 sec^-1
    (omega) = .05 sec ^-1

    What does sec represent? seconds? secant?

    I thought maybe it was .1 seconds raised to the negative 1 power, but the graph I get doesn't match the answer. I'm trying to put the formula into an excel spreadsheet. The full equation is:

    x=x(naught)e^(-beta*time)*[cos(omega*time)+(beta/omega)sin(omega*time)]

    I would appreciate any help on this.

    Thx
     
  2. jcsd
  3. Feb 21, 2004 #2

    Hurkyl

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    In general

    [tex]x^{-1} = 1/x[/tex]

    In particular,

    [tex]\mathrm{sec}^{-1} = 1 / \mathrm{sec} = \mathrm{Hz}[/tex]

    (yes, sec = seconds)
     
  4. Feb 21, 2004 #3
    As Hurkyl said, it is seconds

    Ask yourself this, if it was secant...then wouldn't there have to be a following value?? or are you going to take a secant of nothing?
     
  5. Feb 21, 2004 #4
    Thanks, Hurkyl!
     
  6. Feb 23, 2004 #5

    krab

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    Just a technical point to avoid confusion: Both sec^-1 and Hz are used to denote frequency. However, by convention, Hz stands for cycles per second and sec^-1 is the angular rate (radians per second): they differ by a factor of [itex]2\pi[/itex]. In particular,

    [tex]2\pi\mbox{ sec}^{-1}=1\mbox{ Hz}[/tex]

    Edit: corrected as per NateTG post.
     
    Last edited: Feb 23, 2004
  7. Feb 23, 2004 #6

    NateTG

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    Don't you mean [tex]2\pi s^{-1}=1 \mbox{Hz}[/tex]? 1 Hertz is a cycle per second which is [tex]2\pi[/tex](radians) per second.

    I usually think of [tex]s^{-1}[/tex] as being a unit of angular velocity, and [tex]Hz[/tex] as a unit of frequency.

    Of course, since [tex]2\pi[/tex] is unitless, there can be multiple definitions of [tex]s^{-1}[/tex].

    P.S. [tex]s^{-1}[/tex] is often read as 'per second.'
     
  8. Feb 23, 2004 #7

    krab

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    Sorry. My bad. I'll fix it (like revising the congressional record). I'll attribute it to you so it's clear why you corrected it.
     
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