Transformasi Laplace Transformasi Laplace
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
Transformasi Laplace
Contoh
Contoh
Transformasi dari t n
S I F A T- S I F A T
TURUNAN
Integral. S shifting, T shifting
T Shiting, Convolution, Period
Tabel Laplace
(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) } =
Soal-soal
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
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