(a) Find f(t) given that F(s) = (b) Calculate v(1) given that V(s): s + 12...

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(a) Find f(t) given that F(s) = (b) Calculate v(1) given that V(s): s² + 12 s(s+ 2) (s+3) 10s² + 4 s(s+1)(s+ 2)² (c) Use the Laplace transform to solve the differential equation dv(t) d²v(1) dt² +6- -+8v(t) = 2u(t) dt subject to v(0) = 1. v(0) = -2 (a) Find f(t) given that F(s) = (b) Calculate v(1) given that V(s): s² + 12 s(s+ 2) (s+3) 10s² + 4 s(s+1)(s+ 2)² (c) Use the Laplace transform to solve the differential equation dv(t) d²v(1) dt² +6- -+8v(t) = 2u(t) dt subject to v(0) = 1. v(0) = -2