ABSTRACT
For example, if f t A t( ) = eσ 2 , 0 < t < ∞, the integral will converge if ∞ > σ1 > σ2 > 0. For example, let us nd the Laplace transform of f(t) = Ae−btU(t). is is simply
F s f t t A t A
=
+
∞∫ As b 0
(3.4)
(Note that b is a natural frequency expressed in rad/s; 1/b is a time constant.) As a second example, consider the Laplace transform of the unit step function,
x(t) = U(t).
