quality factor

The quality factor Q of an oscillator is a dimensionless number that measures how slowly it loses energy relative to how fast it oscillates. Formally, Q = ω₀/γ, where ω₀ is the natural angular frequency and γ is the damping rate. Equivalently, Q is roughly the number of oscillations the system completes before its energy falls to 1/e (about 37%) of its initial value.

A high Q means the oscillator rings for a long time. A tuning fork has Q around 1,000 — it sustains a clear tone for many seconds. A quartz crystal oscillator in a wristwatch has Q around 10⁵, which is why it keeps such good time. Atomic clocks reach Q values of 10¹⁰ or more. A low Q means rapid energy loss: a pendulum swinging in water might have Q of 5 or 10.

Q also controls the sharpness of resonance. A high-Q oscillator responds intensely but only within a very narrow band of driving frequencies. A low-Q oscillator responds more broadly but less dramatically. This tradeoff between selectivity and bandwidth runs through all of oscillator physics, from radio receivers to laser cavities.