Answer Happy

Q2 (a) Use the attached Laplace transform table to find the Laplace transform of each of the following functions. In each case, calculate the location(s) of the pole(s) and sketch these on an s-plane diagram. (i) fr(t) = 25 e-10 (3 marks) (ii) fz(t) = 10 sin(10000 a t) + 8 cos(10000 4 t) - (6 marks) (b) A second order system has an s-domain function H(s) given below. H(s) = 40(s +200) s? + 400 s + 6290000 (i) Calculate the locations of the poles of H(s), and sketch these on an s-plane diagram. (4 marks) (ii) Given that a standard form for a second order system denominator is: s? + 2¢0, s + 0,2 calculate the damping factors and natural frequency O, for system H(s) defined above. State the type of damping this system has. (6 marks) (ii) Use the attached Laplace transform table to determine the impulse response h(t) of the system defined above, i.e. find the inverse Laplace transform of H(s). (6 marks) TOTAL FOR Q2:25 marks