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    Matlab Laplace Transform 1

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    Tarik Tawfeek
    Matlab Laplace Transform 1

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    Matlab Laplace Transform 1

    Uploaded by

    Tarik Tawfeek
    2 views16 pages
    Matlab Laplace Transform 1

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    Matlab Laplace Transform 1

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    2 views16 pages

    Matlab Laplace Transform 1

    Uploaded by

    Tarik Tawfeek
    Matlab Laplace Transform 1

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
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    Laplace Transform

    Learning Outcomes
    ⚫ At the end of the present lecture the student will be
    able to:
    ⚫ - Convert the time domain equations To S domain
    ⚫ -Taking the inverse of Laplace transform
    ⚫ -Applying the partial fraction
    ⚫ -Solve the differential equation using Laplace
    transform
    Laplace Transformation

    L[ f (t )] = F ( s)

    F ( s) =  f (t )e dt
    − st
    0

    −1
    L [ F ( s )] = f (t )
    L

    F(t) F(S)
    Time Domain S or Laplace Domain

    L-1
    Differential Equation

    Figure 1.
    Steps involved Transform differential
    in using the equation to
    algebraic equation.

    Laplace
    transform.
    Solve equation
    by algebra.

    Determine
    inverse
    transform.

    Solution
    Illustration of the unit step function.

    u (t )

    0 t
    Derive the Laplace transform of the
    unit step function

    F ( s) =  (1)e dt
    − st
    0


    e 
    − st
    e  1 −0
    F ( s) =  = 0− =
    −s  0  −s  s
    Types of inputs
    Convert functions from time domain to S domain
    Example 1. A force in newtons (N) is given below.
    Determine the Laplace transform.

    f (t ) = 50u (t )
    50
    F (s) =
    s
    Example 2. A pressure in pascals (p)
    starting at t = 0 is given below.
    Determine the Laplace transform.
    −4 t
    p (t ) = 5cos 2t + 3e

    s 1
    P( s ) = L[ p(t )] = 5  2 + 3
    s + (2) 2
    s+4
    5s 3
    = 2 +
    s +4 s+4
    Example 3. A voltage in volts (V) starting
    at t = 0 is given below.
    Determine the Laplace transform.
    −2 t
    v(t ) = 5e sin 4t

    4
    V ( s ) = L[v(t )] = 5 
    ( s + 2) + (4)
    2 2

    20 20
    = 2 = 2
    s + 4s + 4 + 16 s + 4 s + 20
    Inverse Laplace Transforms
    by Identification
    ⚫ When a differential equation is solved by
    Laplace transforms, the solution is obtained
    as a function of the variable s.

    ⚫ The inverse transform must be formed in


    order to determine the time response.
    Example 1. Determine the inverse
    transform of the function below.
    5 12 8
    F ( s) = + 2 +
    s s s+3

    −3t
    f (t ) = 5 + 12t + 8e
    Example 2 Determine the inverse
    transform of the function below.
    200
    V ( s) = 2
    s + 100

     10 
    V ( s) = 20  2 2 
     s + (10) 

    v(t ) = 20sin10t

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