The unit of s (Laplace complex frequency)

Thread Starter

logicman112

Joined Dec 27, 2008
69
My question is about Laplace transform. We integrate f(t)e^(-st).
We know that the unit of s is radian/second and t is second. So what is the meaning of e^radian?
Like e^(3 radian)?
 

shteii01

Joined Feb 19, 2010
4,644
Quoting from Electric Circuits by J. W. Nilson and S. A. Riedel:
"In our applications, t represents the time domain, and, because the exponent of e in the integral must be dimensionless, s must have the dimension of reciprocal time, or frequency."

In other words, Laplace Transform does not have units, it is a mechanism, not a goal. Time goes in, frequency comes out. Inverse Laplace Transform, frequency goes in, time comes out.
 

edgetrigger

Joined Dec 19, 2010
133
angular velocity radians per sec
and time is the duration

so rad/sec* t in secs will give you radians.

eg: s = 5rad/sec and duration t = 5 sec

then s*t = 5rad/sec * 5 = 1 rad

comparison is like this

if you are driving a car at 60 miles per hour and drive for 10mins then
distace travelled by you is 60 miles/60mins * 10 mins = 10 miles

all the mins gone left with miles.
 
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