Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:


    I would appreciate any help on this.

  2. jcsd
  3. Feb 21, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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


    User Avatar
    Science Advisor

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook