CET4846 Spring 2021 Homework #2 (Time Domain Properties) - 100 points 1. a) Write the general Laplace form for all of these Transfer functions: 400 a. G(s) 52 + 12s + 400 900 b. G(s) = 52 + 90s + 900 225 c. G(s) = 2+30s + 225 32 +625 625 d. G(s) 52 b) Based on the value of (zeta) determine if the system is undamped, underdamped, overdamped, or critically damped. c) plot the TF on the s-plane and make sure your assessment of each system in b) is correct 50 5+50 2. For this 1" order system: G(s) = a) Find the time domain step response c(t) = L-?[G(s) R(s)] b) Find the Settling Time, Rise Time, and Time constant for this system 3) Write the Time domain step response for all the functions. Hint (you should be able to do this by just looking at the functions without having to calculate the inverse laplace transformation by hand.) Prob 17d, e, f a) G(s) = (s? +65 +144) b) G(s) = (52 +9) c) G(s) = (s+10) 20 S+2 5+5 4) Find the Settling Time, Rise Time, %OS, Peak Time for all TFs in Problem 3