What is the damping factor?

What is the damping factor?

• A. The natural frequency
• B. The damping factor
• C. The time constant
• D. The steady-state gain

Answer: (B)

The damping factor is the damping ratio, a dimensionless measure of how strongly a system is damped relative to the amount needed for critical damping. In a mass–spring–damper, it’s defined as zeta = c / (2 sqrt(mk)); in the standard second-order form x'' + 2 zeta omega_n x' + omega_n^2 x = 0, omega_n = sqrt(k/m) is the natural frequency. This ratio determines the transient behavior: if zeta < 1, the system is underdamped and the response oscillates with decaying amplitude; if zeta = 1, it is critically damped and returns to equilibrium as fast as possible without oscillating; if zeta > 1, it is overdamped and returns to equilibrium without oscillating but more slowly. The damping factor is distinct from the time constant (a first-order concept) and from steady-state gain (the final value to a steady input).

The damping factor is the damping ratio, a dimensionless measure of how strongly a system is damped relative to the amount needed for critical damping. In a mass–spring–damper, it’s defined as zeta = c / (2 sqrt(mk)); in the standard second-order form x'' + 2 zeta omega_n x' + omega_n^2 x = 0, omega_n = sqrt(k/m) is the natural frequency. This ratio determines the transient behavior: if zeta < 1, the system is underdamped and the response oscillates with decaying amplitude; if zeta = 1, it is critically damped and returns to equilibrium as fast as possible without oscillating; if zeta > 1, it is overdamped and returns to equilibrium without oscillating but more slowly. The damping factor is distinct from the time constant (a first-order concept) and from steady-state gain (the final value to a steady input).