Transformasi Laplace Transformasi Laplace.

Presentasi berjudul: "Transformasi Laplace Transformasi Laplace."— Transcript presentasi:

1 Transformasi Laplace Transformasi Laplace

2 Transformasi Laplace. Definisi : Misalkan f(x) fungsi yang ditentukan untuk semua t yang positip, maka : F( s ) = dinamakan Transformasi Laplace dari f( t ) dan ditulis

3 Transformasi Laplace

4 Contoh

5 Contoh

6 Transformasi dari t n

7 S I F A T- S I F A T

8 TURUNAN

9 Integral. S shifting, T shifting

10 T Shiting, Convolution, Period

11 Tabel Laplace

12 (ii) L{ a f1(t) + b f2(t) } = a L{ f1(t) } + b L{ (t) }   Bila L{ f (t) } = F ( s ) maka :   (iii)  L{ e at f(t) } = F ( s – a ) (iv)  L{ tn f(t) } = (-1)n (v)   L{ f(t) } =

13 Soal-soal

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19 Unit Step Function L{u(t)}= Useful for representing sudden changes
1 time (sec) u(t) L{u(t)}= sin(wt) u(t) 1 time Useful for representing sudden changes sin(wt)u(t) e.g. application of sinusoid at t = 0 time EC&S CHAPTER 2

20 approximation to unit impulse representation of ideal unit impulse
d(t) time (sec) DT approximation to unit impulse area = 1 1 Unit Impulse Function Mathematical representation of short burst of input (lightning, hammer blow, etc.) Exact shape unimportant if duration short relative to effects L{d(t)} = = 1 time (sec) representation of ideal unit impulse Impuse functions sometimes used to test system dynamics EC&S CHAPTER 2