Solving sec^-1 in Horizontal Displacement Equation

[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

 

[Hurkyl]

In general

x^{-1} = 1/x

In particular,

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

(yes, sec = seconds)

 

[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?

 

[gskroger]

Thanks, Hurkyl!

 

[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.

 

[NateTG]

Originally posted by 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,

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

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.'

 

[krab]

Originally posted by NateTG
Don't you mean 2\pi s^{-1}=1 \mbox{Hz}?

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.