Question

For a second-order system subjected to a step input, which situation(s) below experience oscillations or overshoot?

O Undamped
O Underdamped
O Critically damped
O Overdamped
- a and b
- a, b and c
- c and d
- b, c, and d
- All of the above

Answer 1

Underdamped systems experience oscillations and overshoot when subjected to a step input, whereas overdamped systems do not oscillate but approach equilibrium more slowly. Critically damped systems return to equilibrium quickly without oscillating.

Step-by-step explanation:

For a second-order system subjected to a step input, the situations that experience oscillations or overshoot are those where the system is either underdamped or has less-than critical damping. An underdamped system, characterized by a small damping constant (b < √√4mk), moves quickly towards equilibrium but overshoots due to oscillations around the equilibrium point and the amplitude of the motion decays exponentially.

In contrast, an overdamped system, where the damping constant is large (b > √4mk), will not oscillate but will approach equilibrium much more slowly than both underdamped and critically damped systems. Critical damping occurs when b = √4mk, and in this state, the system returns to equilibrium as quickly as possible without any oscillations.