
resulting in sustained oscillations from 0 to 2 when K ¼1. The differential equation of the unforced
system is
d
2
dt
2
y(t) þ v
2
n
y(t) ¼ 0 (2:28)
and the natural response resulting from the presence of initial conditions is that of harmonic motion,
that is, sustained oscillations about zero at a frequency of v
n
rad=s.
Except for the case when z ¼0, the unit step response approaches the limiting or steady-state
value y(1) ¼K, which means that K is the DC or steady-state gain of the second-order system in
Equation 2.16. The parameter z, which determines the existence and extent of the oscillations as
well as the duration of the transient response, is called ...