Editing Resonance (section)

==== The pendulum ====
For other driven, damped harmonic oscillators whose equations of motion do not look exactly like the mass on a spring example, the resonant frequency remains
<math display="block">\omega_r = \omega_0 \sqrt{1 - 2\zeta^2},</math>
but the definitions of ''ω''<sub>0</sub> and ''ζ'' change based on the physics of the system. For a pendulum of length ''ℓ'' and small displacement angle ''θ'', Equation ({{EquationNote|1}}) becomes
<math display="block"> m\ell\frac{\mathrm{d}^2\theta}{\mathrm{d}t^2} = F_0 \sin(\omega t)-mg\theta-c\ell\frac{\mathrm{d}\theta}{\mathrm{d}t}</math>

and therefore
* <math>\omega_0 = \sqrt{\frac{g}{\ell}},</math>
* <math>\zeta = \frac{c}{2m}\sqrt{\frac{\ell}{g}}.</math>