g(t) = { 4. (Q4] 20 points (a) If the function f is defined by t, 0 /2 i. 03 pts Show that the function f c

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G T 4 Q4 20 Points A If The Function F Is Defined By T 0 T 2 2 T 2 I 03 Pts Show That The Function F C 1 (26.41 KiB) Viewed 44 times

g(t) = { 4. (Q4] 20 points (a) If the function f is defined by t, 0<t</2 */2, t> /2 i. 03 pts Show that the function f can be written as g(t) = -(t - #/2)U(t – 7/2) where U is the unit step function ii. 05 pts Find the Laplace Transform of g(t) iii. 05 pts Find the inverse Laplace Transform of 1 G(3) (s - 2)2 +1 (b) 07 pts Using Laplace Transform find the solution of the differential equation y" + 5y = g(t), y(0) = 4, 7(0) = 0 where g(t) = { ={. 7/2, 0 <t</2 t> /2