Laplace and Non steady state signals?

[PhillDubya]

Hey everyone, hope your Christmas was well, and a good New Years too.

Quick question...

What would be a NON steady state sin wave?

I am trying to visualize it... I understand steady state, and I certainly understand a sin wave, but what exactly is a sin wave where you would apply the σ variable in your Laplace equation for: s≡σ+jω?

Normally, when using the Laplace transform for transfer functions, you always get rid of the σ, by having σ=0 and use s=jω, because it is understood that theoretically you are using Steady State signals, and their in lies my question...What exactly would a non steady state sinusoidal voltage be, where you incorporate σ = e^σt?



Thanks

 

[Papabravo]

A negative real part corresponds to a decaying exponential. So the amplitude of the sine wave would decay forever without reaching zero.

In the systems business we observe that: "the positive real roots of the characteristic equation disappear, or the system does".

 

[MrAl]

Hi there,


Here is a quick illustration of what that looks like.

Note that σ is actually negative in this picture. If it was
positive the wave would ramp up instead of down.

 

[PhillDubya]

I understand now, thanks.