solve the following questions ( handwritten solution only neatly and clean box final answer) thankyou!

Find F(s) a. f (1) = - e" cost + tsin 2 + -t' + cosht + 5e-* 4 OSIs2 b. f ( 1 ) = 1 1 + 2 1> 2 c. f (t) = (12 + e2 + sinta(t - 1) Find f (1) 5s +1 2s a. F(s) = $2 + 25 + 5 (s? + 1 ) 2 b. F(s) = +1)e-z Find x(t) using Laplace transform x"(t) - 4x'(t) + 4x(t) = 4cos2t x(0) = 2, x'(0) =5 Find x(t) x" (t) + x(t) = F(t) 4 0Sis2 F (1 ) = + 2 1>2 x(0) = 0, x' (0) = 0 Problem An 8-1b weight attached to a spring exhibits simple harmonic motion. Determine the equation of motion if the spring constant is 1 ib/ft and if the weight is released 6 inches below the equilibrium position with a downward velocity of 3/2 ft/s. Express the equation of motion in the form Asin(wt + $)