quality:correction, information:extraction
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 ω r = ω 0 1 − 2 ζ 2, {\displaystyle \omega _{r}=\omega _{0}{\sqrt {1-2\zeta ^{2}}},} but the definitions of ω and ζ change based on the physics of the system. For a pendulum of length ℓ and small displacement angle θ, Equation (1) becomes m ℓ d 2 θ d t 2 = F 0 sin (ω t) − m g θ − c ℓ d θ d t {\displaystyle 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}}}

and therefore