Laplace Transform - Sigma+jw | Control Theory Explained

AI Thread Summary
The discussion focuses on the physical significance of the complex variable sigma + jω in the context of the Laplace transform and control theory. Sigma represents the real part, indicating system stability and exponential growth or decay, while ω represents the imaginary part, associated with oscillatory behavior and frequency response. For example, if sigma equals 4 and omega equals 5 rad, it suggests a system with a specific growth rate and oscillation frequency. Understanding these components helps in analyzing system dynamics and response characteristics. The conversation emphasizes the importance of these parameters in control theory applications.
shankarnus
Messages
3
Reaction score
0
Hi guys..:)

I have a doubt regarding laplace transform.
can anyone tel me... what is the physical significance of sigma+jw in it...?
what interpretations we can make from sigma and jw in control theory...?
 
Mathematics news on Phys.org
Well, do you mean this?

\sigma + j \omega

Here, \sigma is the real part and \omega is the imaginary part of a complex number...
 
First thank u soo much for ur kind reply...:)

ya the same...i need to know the physical significance of it...:)

for why we r goin for it...:)
 
k...if sigma=4 and then omega=5 rad..

then wat we can say from it...? wat does it indicate
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Back
Top