aplikasi transformasi laplace (1).pdf
TRANSCRIPT
-
Aplikasi Transformasi Laplace (1)
-
Penyelesaian Persamaan diferensial
Consider an initial value problem
Where a and b are constant.
Here r(t) is the given input (driving force) applied to the mechanical or electrical system and y(t) is the output (response to the input) to be obtained.
-
Penyelesaian persamaan differensial
Step 1 : Setting up the subsidiary equation.
-
Step 2 : Solution of the subsidiary equation by algebra called transfer function
Step 3. Inversion of Y to obtain y.
-
Contoh
Selesaikan
y y = t, y(0) = 1, y(0) = 1
Penyelesaian
Step 1 : subsidiary equation
[s2Y(s) sy(0) y(0)] Y(s) = 1/s2
[s2Y(s) s 1] Y(s) = 1/s2
(s2 1) Y(s) = s + 1 + 1/s2
-
Step 2 : transfer function Q = 1/(s2 1)
Step 3 : Obtain Solution
-
Contoh lain
Selesaikan
y" + y' + 9y = 0, y(0) = 0.16, y'(0) = 0.
Penyelesaian
[s2Y - 0.16s] + [sY- 0.16] + 9Y = 0,
(s2+ s + 9)Y = 0.16(s + 1).
-
Shifted data problem
Selesaikan
y + y = 2t, y(/4) = , y() = 2 - 2
Karena t0 = , maka kita set t = t +
y + y = 2(t + ), y(0) = ; y(0) = 2 - 2
Penyelesaian
-
Shifted data problem (2)
maka
karena
-
Contoh 3
Selesaikan
y + y = t, y(0) = 1 dan y(0) = -2
Penyelesaian
[s2Y - sy(0) y(0)] + Y = 1/s2
(s2+1) Y = 1/s2 + s -2
Y
y = t + cos t -3 sin t
-
Contoh
Tentukan arus i(t) pada rangkaian RC berikut, jika diterapkan gelombang kotak v(t) seperti pada gambar
-
v(t) = V0[u(t - a) - u(t - b)].
Transformasi laplace
dengan
-
Penyelesaian
-
Latihan
Selesaiakan