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ENGR5001 / Week 3
ENGR201 Laplace deck example 1, piecewise signal built from stepsTutorialOld spec ENGR2012:25 min

ENGR201 (old spec) Laplace transforms deck, Example 1 (page 14)

The signal f(t)f(t) in the figure is 0 for t<1t < 1, equal to 1 for 1≤t<21 \le t < 2, equal to 2 for 2≤t<32 \le t < 3, and 0 again for t≥3t \ge 3. Construct f(t)f(t) using unit step (Heaviside) functions and find its Laplace transform. As a check, evaluate F(s)F(s) at s=1s = 1.

f(t): 0 until t = 1, then 1 until t = 2, then 2 until t = 3, then 0.
f(t): 0 until t = 1, then 1 until t = 2, then 2 until t = 3, then 0.
Formulas you may need
  • L[u(t−c)]=e−css\mathcal{L}[u(t - c)] = \dfrac{e^{-cs}}{s} (learn this)