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()

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)

a) make the Inverse Laplace Transform of the given function. Show all decals in detail and simplify the result completely. 8s +3 F(s) = (s + 1)2(2s² + 16s + 30) b) make the Laplace Transform of the given function. f(t) = 6te-3t + te-5t sin5t + t?

5. Find the inverse Laplace transforms of the functions given. Accurately sketch the time functions. 3e-2s a) F(s) = s(s+3) e-2s b) F(s) = s(s+1) e-28-e-3s c) F(s) = 2

Question 2 a. Determine the Laplace Transform of the following functions: e4t (t2 + 3t + 5) b. Determine the Inverse Laplace Transform of the following functions: (-금+금) 2 s+1,

Find the inverse Laplace transform of the following functions: s2 + 6s + 8 G(s) = s4 + 8s2 + 16 Your answer must contain detailed explanation, calculation as well as logical argumentation leading to the result. If you use mathematical theorem(s)/property(-ies) that you have learned par- ticularly in this unit, clearly state them in your answer.