The unit of s (Laplace complex frequency)

Discussion in 'Math' started by logicman112, Jan 4, 2011.

  1. logicman112

    Thread Starter Active Member

    Dec 27, 2008
    69
    2
    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)?
     
  2. shteii01

    AAC Fanatic!

    Feb 19, 2010
    3,378
    494
    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.
     
    anhnha likes this.
  3. edgetrigger

    Member

    Dec 19, 2010
    133
    19
    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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