Laplace+TransferFunctions

M.D. Bryant ME 344 notes 03/25/08 3
Procedure:
• Convert Linear Differential Equations
x ˙ = Ax + f (t)
d n x d n"1 x d 2 x d x
+ a
dt n n"1
+!+ a
dt n"1 2
+ a
dt 2 1
dt
+ a
0
x = f (t)
!
in time t into algebraic equations in
complex variable s, via forward Laplace
transforms:
X(s)=L {x(t); t → s }, F(s)=L {f(t); t → s }
• Solve resulting algebraic equations in s,
for solution X = X(s)
• Convert solution X(s) into time function
x(t), via inverse Laplace transform:
x(t) = L -1 {X(s); s→ t }