ENGR201 Laplace deck examples, inverse transforms with distinct real poles (ENGR5001)

ENGR201 Laplace deck examples, inverse transforms with distinct real polesTutorialOld spec ENGR201Third8 min

Find the inverse Laplace transforms:

Formulas you may need

$\mathcal{L}^{-1}\left[\dfrac{1}{s + a}\right] = e^{-at}$ ; linearity of $\mathcal{L}^{-1}$ (learn this)
Partial fractions: one term $\dfrac{A}{s + p}$ per distinct linear factor (learn this)

(a)
$\mathcal{L}^{-1}\left[\dfrac{1}{(s + a)(s + b)}\right]$ , where $a \ne b$ are constants
(b)
$\mathcal{L}^{-1}\left[\dfrac{s + 1}{(s + 2)(s + 3)}\right]$ , and its value at $t = 1$
f(1) =