Question

need help please write out your steps thank you

Find the Ivesm s) of the general F(S)= IIS-los +100 Your answer should be a fonction of retns fom tncton 1 t( 2

Answer 1

11s^2 - 10s + 100/s (s^2 + 25) = A/s + BS + c/s^2 + 25 11s^2 - 10s + 100 = A (s^2 + 25) + (BS + c) s = As^2 + 25A + Bs^2 + cs 11s^2 - 10s + 100 = (A + B) s^2 + cs + 25A equating co-efficient of s, s^2 and constant term, we get 25A = 100 c = -10 11 = A + B A = 100/25 = 4 B = 11 - 4 = 7 11s^2 - 10s + 100/s (s^2 + 25) = 4/5 + 7s - 10/s^2 + 25 = 4/5 + 7s/s^2 + 25 - 10/s^2 + 25 L^-1[11s^2 - 10s + 100/s(s^2 + 25)] = L^-1 (4/5) + L^-1 (7s/s^2 + 25) - l^-1 (10/s^2 + 25) = 4.L^-1 (1/s) + 7 L^-1 (s/s^2 + 5^2) - 2 L^-1 (5/s^2 + 5^2) = 4 + 7 cos 5t - 2 sin 5t