1) Find the Laplace transforms of the following time functions. Solve problem 1(a) and 1 (b)...

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1) Find the Laplace transforms of the following time functions. Solve problem 1(a) and 1 (b) using the Laplace transform definition i.e. integration. For problem 1(c) and 1(d) you can use the Laplace Transform Tables. a) f(t) = 1 + 2t b) f(t) = sin wt [Hint: Use Euler's relationship, sin wt c) f(t) = sin(2t) + 2 cos(2t) + et sin(2t) d) FPE Problem 3.5 (d) b) F(s) = 2) Find the time functions corresponding to each of the following Laplace transforms using partial fraction expansions (PFE): a) F (s): 10 s(s+1)(s+10) = 3s² +9s+12 (s+2) (s2+5s+11) ejat-e-jwt 2j 1) Find the Laplace transforms of the following time functions. Solve problem 1(a) and 1 (b) using the Laplace transform definition i.e. integration. For problem 1(c) and 1(d) you can use the Laplace Transform Tables. a) f(t) = 1 + 2t b) f(t) = sin wt [Hint: Use Euler's relationship, sin wt c) f(t) = sin(2t) + 2 cos(2t) + et sin(2t) d) FPE Problem 3.5 (d) b) F(s) = 2) Find the time functions corresponding to each of the following Laplace transforms using partial fraction expansions (PFE): a) F (s): 10 s(s+1)(s+10) = 3s² +9s+12 (s+2) (s2+5s+11) ejat-e-jwt 2j

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