Problem 6 Find the Laplace transform of the functions f(t) listed below by the following figures: b. the function f(t) in the Figure 2. c. the function f(t) in the Figure 3. f(t) A T 0 T f(t) Figure 2: f(t) 26 a a 0 #2 --- Figure 3: f()

1 3 Using definition, determine the Laplace Transform of the function represented by the graph shown above. 2.

Part II. Find the Inverse Laplace Transform of the following: 8s2-4s+12 1. F(s) s3 +4s

2. Determine the Laplace transform of the following functions. Here you may use common identities and known transforms of basic functions, but clearly show each step and briefly state which identities/properties you use in each step (i.e. Shift Theorems, Derivative Theorem etc.). f(t) = te-2t cos(4t) f(t) = t² sin2(t) + t cos² (t)