Figure 6.1: Damped oscillations.displaced from its equilibrium position, then it will slowly move toward equilibrium, but will not overshoot
it, so no oscillations will occur. In this case the motion is described by
x.t/De.b=2m/t.AeCtCBeCt/; (6.4)whereCD
q
.b=2m/^2 !^20 , and the constantsAandBdepend on the initial conditions. This case is also
illustrated in Fig. 6.1.
6.3 Critically Damped
In between the underdamped and overdamped case is the case ofcriticaldamping, where the damping con-
stantbD2m! 0. In this case, the mass returns to its equilibrium position as quickly as possible, without
overshooting. The motion in this case is
x.t/De.b=2m/t.AtCB/; (6.5)where again the constantsAandBdepend on the initial conditions. Fig. 6.1 shows critical damping compared
to the similar-looking overdamped case.