Question: Starting with Eq. 5.51, derive expressions for the following response characteristics of the underdamped second-order system.(a) The time to first peak t (Eq. 5-52).(b) The

Starting with Eq. 5.51, derive expressions for the following response characteristics of the underdamped second-order system.(a) The time to first peak t (Eq. 5-52).(b) The fraction overshoot (Eq. 5-53).(c) The decay ratio (Eq. 5.54).(d) The settling time (ts, defined in Fig. 5.10). Can a single expression be used for ts, over the full range of ?, 0 (5-51) y() = KM cos sin V1 - Time to first peak:

(5-51) y() = KM cos sin V1 - Time to first peak: tp = TT/VI - OS = expl - nt/i - (5-52) %3D Overshoot: (5-53) exp(-2mt//1- ) DR = (OS)? Decay ratio: (5-54)

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