NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/  September 18, 2019, 04:49:56 pm  Welcome, Guest. Please login or register.Did you miss your activation email? 1 Hour 1 Day 1 Week 1 Month Forever Login with username, password and session length Home Help Search Login Register
"In theory, theory and practice are the same. In practice, they are not." ..."Albert Einstein (1879~1955, Mathematical physicist, Nobel Prize 1921-Physics)"
 Pages:    Go Down Author Topic: Complex numbers and Laplace transform  (Read 13343 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
j142
Newbie  Offline

Posts: 11 « Embed this message on: June 24, 2009, 09:01:50 am » posted from:Ahmadabad,Gujarat,India what is use of complex numbers?

what is a physical meaning of complex numbers?

what is Laplace transform? and what is a physical meaning of that also? Logged
Fu-Kwun Hwang
Hero Member      Offline

Posts: 3082   « Embed this message Reply #1 on: June 24, 2009, 06:37:56 pm » posted from:Taipei,T\'ai-pei,Taiwan The complex numbers are solution for mathematics equation.
The physics meaning of complex number depends on how and where you use it.
For example: There is a 90 degree phase between voltage and current for inductor and capacitor.
The inpedance for an inductor is represented as $j\omega L$, and impedance for a capacitor is represent as $\frac{1}{j\omega C}$, where $j=\sqrt{-1}$.
For an R-L-C series circuit, the total impedance is $Z=R+j(\omega L-\frac{1}{\omega C})$.
The impedance Z is a complex number which means that there is a phase shift between current flow thrugh the circuit and the total voltage applied to the circuit.

Many calculation become easier with the help of complex number.

We need to solve differential equation for many different problems.
Some of those might not be easy to solve.
However, if we make a Laplace/Fourie transform, the differential/integral equation become multiple/divide operation.
In many cases, it is much easier to solve it this way and find out it's solution.
Then, we can make a inverse transformation to get it solution to the coordinate system we are more familiar with.

For example: We measure sound wave as a function of time and the singal can be shown in oscilloscope.
However, it is not easy to find information from the sound wave directly.
If the sound wave was being transofrmed to frequence space (Fourier transform). Then, it is much easier to find out the characteristic pattern for different music instrument ( and different personal have unique frequence pattern,too). So there are many different transformation tools help us to transoform our data from one representation to another representation (Just like look at the same event from different point of view).
It seems that engineer use more Laplace transform(decay system) and physicist use more Fourier transform (oscillation system). Logged
 Pages:    Go Up
"In theory, theory and practice are the same. In practice, they are not." ..."Albert Einstein (1879~1955, Mathematical physicist, Nobel Prize 1921-Physics)"
 Related Topics Subject Started by Replies Views Last post  how technology can be used to transform education in 21st century learning Questions related to EJS lookang 5 15322 February 12, 2010, 08:38:47 pm by Fu-Kwun Hwang  RLC AC + Laplace surface with poles and zeros Request for physics Simulations lcaruso 0 5264 October 24, 2009, 08:54:10 am by lcaruso  How can i transform a 3D cylinder using 2 transformation with dynamic variables Questions related to EJS lookang 2 7464 November 09, 2009, 08:01:49 pm by lookang  how to transform about an axis a rotation using Matrix3DTransformation ? Questions related to EJS lookang 2 16413 August 24, 2012, 03:16:04 pm by lookang
Page created in 0.366 seconds with 23 queries. since 2011/06/15