EQUATION

Quality Factor (Q)

Q = ω₀/γ characterizes how sharply an oscillator resonates

§ 01

The equation

EQ.Q-FACTOR
Q = \frac{\omega_0}{\gamma}
§ 02

What it solves

Q = ω₀/γ characterizes how sharply an oscillator resonates. A high Q means narrow bandwidth, slow energy decay, and many cycles before the amplitude halves. A guitar string has Q ~ 1000; a car shock absorber has Q ~ 0.5.

§ 03

When to use it

Comparing damping across oscillators, calculating bandwidth Δω = γ = ω₀/Q, or estimating how many oscillations occur before significant decay. Q also appears in the resonance amplitude formula: A_res = (F₀/m)/(γω₀).

§ 04

When NOT to use it

Q is defined for underdamped oscillators. Critically and overdamped systems (Q < ½) do not resonate in the usual sense. The Q defined here (mechanical Q) differs from the electrical Q in circuits by a sign convention in some textbooks — verify the definition being used.

§ 05

Common mistakes

Inverting the formula to Q = γ/ω₀. Confusing bandwidth Δω = γ with half-bandwidth = γ/2. Using Q without checking whether the oscillator is actually underdamped — Q > ½ is required for oscillatory behavior.

§ 06

Topics that use this equation

§ 07

Problems using this equation