What is the physical meaning of Laplace operator? 1

[jsboy]

According to some dynamics book, it says the 2nd differential equation can be transformed to just a simple algbraic equation by applying Laplace transformation and I know how it works and what is the beneit of doing that in terms of the ease of caluculation. However what I want to know is the physical meaning of Laplace transform and how it is related to tranfer function. I want to know someting that is not explained in basic dynamics book about Laplace.

 

[hacksaw]

transforms represent a one-to-one mapping between the time and frequency response of linear systems.

the frequency response is algebraic as opposed to solving differential equations in time, and is simpler to work with.

 

[electricpete]

Differential equation:
mx''+cx'+kx = f(t)

algebraic Laplace equation
ms^2X(s) + cX(s)+ kX(s) = F(s)
assumed x(0)=x'(0)=0.

Laplace transfer function:
H(s) = X(s)/F(s) = 1 / [ms^2+cs+k]

Fourier transfer function: substitute s=jw
H(w) = X(w)/F(w) = 1 / [-mw^2+jcw+k]

Physical meaning of the fourier transfer function (function of frequency): gives complex amplification factor of the system for sinusoidal input.

 

[MikeyP]

Physical meaning?

It is a mathematical tool - like complex arithmetic.

Would you ask the question, "What is the physical meaning of complex arithmetic?"?

(maybe you would?!?!)

M

--
Dr Michael F Platten