Create two-pole system transfer functions designed to meet the requirements indicated in each part below.

(a) Assume a sample period of T 0.02 seconds, a DC gain of 1, a zero at the origin, a percent overshoot of 20% or less, and a 1% settling time of 0.5 seconds or less.
(b) Assume a sample period ofT 0.02 seconds, a DC gain of 1, a zero at the origin, a percent overshoot of 10% or less, and a peak time of 0.2 seconds or less.
(c) A DC gain of 1, a zero at the origin, a peak time of 6 sample periods or less, and a settling time of 35 sample periods.
(d) Assume a sample period of T 0.05 seconds, a DC gain of 1, a zero at the origin, and a 1% settling time of 0.8 seconds or less.