# What does sec^-1 mean?

1. Feb 21, 2004

### gskroger

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. Feb 21, 2004

### Hurkyl

Staff Emeritus
In general

$$x^{-1} = 1/x$$

In particular,

$$\mathrm{sec}^{-1} = 1 / \mathrm{sec} = \mathrm{Hz}$$

(yes, sec = seconds)

3. Feb 21, 2004

### Spectre5

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?

4. Feb 21, 2004

### gskroger

Thanks, Hurkyl!

5. Feb 23, 2004

### krab

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 $2\pi$. In particular,

$$2\pi\mbox{ sec}^{-1}=1\mbox{ Hz}$$

Edit: corrected as per NateTG post.

Last edited: Feb 23, 2004
6. Feb 23, 2004

### NateTG

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

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

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

P.S. $$s^{-1}$$ is often read as 'per second.'

7. Feb 23, 2004

### krab

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.