M427K Handout: Applications of the Laplace Transform: ExamplesSalman ButtMarch 23, 2006Notes1. If you have any friends in engineering (or geology) that are graduating and looking for afull-time position, URS Corporation is hoping to hire a significant number of new employees.I have a friend who works there, and putting her name down as a reference on their onlineform would be helpful to your friends’ applications. The name is Erica Allis.Examples1. Sketch the graphs of the following functions on the interval t ≥ 0:u1(t) + 2u3(t) − 6u4(t) u3(t) sin(t − 3)2. Find the Laplace transform of the following function:f(t) =0, t < 1t2− 2t + 2, t ≥ 113. Find the inverse Laplace transform of the following function:F (s) =2(s − 1)e−2ss2− 2s + 24. Solve the following initial value problem:y00+ y = f(t), y(0) = 0, y0(0) = 1, f(t) =1, 0 ≤ t < π/20, π/2 ≤ t <
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