Exploring Applications of Laplace Transformations in Various Systems

[wr8_utd]

Hey
I'm new here. Well we're currently doing Laplace in our Maths lectures. Now the Teacher has set us a project on Laplace and we need to find some applications of Laplace Transformations.

Can anyone tell me some specific areas where Laplace is applied. I remember reading somewhere it's used in a mass spring damper system.

Are there any other examples of machines or something where Laplace is used?

Help would be greatly appreciated!

 

[wr8_utd]

Laplace DLTS is one application right?

 

[Mike_In_Plano]

Laplace transforms are a Godsend for engineers. Any time energy storage elements are tossed into an engineering problem, differential equations arise. For example, springs, potential energy, kinetic energy, capacitors (charge storage energy), inductors (magnetic storage).
Usually on energy storage element isn't too bad to deal with, and two can be managed with standard forms, but anything above that is generally too messy for a closed form, time domain solution.
That's where the Laplace domain comes in. Using straight algebraic operators in the Laplace domain makes these problems simple.

 

[lennybogzy]

Laplace transforms are a Godsend for engineers. Any time energy storage elements are tossed into an engineering problem, differential equations arise. For example, springs, potential energy, kinetic energy, capacitors (charge storage energy), inductors (magnetic storage).
Usually on energy storage element isn't too bad to deal with, and two can be managed with standard forms, but anything above that is generally too messy for a closed form, time domain solution.
That's where the Laplace domain comes in. Using straight algebraic operators in the Laplace domain makes these problems simple.

that's exactly right. any time you're analysing something whos properties are determined by a change of somethign else (current through capacitor is a function of the change of voltage [frequency]) etc, the only way to express it is via a differential equation. The easiest way to deal with those differential equations is by transforming them into a frequency domain via laplase, and using simply algebraic manipulation.

However, don't forget that the real world has programs and websites so put your slide ruler away.

 

[Naty1]

check this out: http://en.wikipedia.org/wiki/Laplace_transform_applied_to_differential_equations

and follow the link LINEAR DIFFERENTIAL EQUATIONS too...

 

[klondike]

As long as the system to be investigated is linear and time invariant (Linear ODE with CONSTANT coeffs), Laplace Transform is your friend.

Many engineering problems in control systems, feedback systems are more conveniently analyzed in S domain than in the time domain and often yield better insights.