The response of a second order system depends on the value of the damping ratio . For the system is underdamped and the response is oscillatory even for a steady input. For the system is critically damped and for it is overdamped. If the response is gradual and non-oscillatory with no overshoot (Figure 2.22). The system reaches steady state monotonically at the fastest rate if . We have the following results for a second order system subject to a step input:

Here the natural frequency and the phase lag for . For a periodic input: