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Single-Degree-of-Freedom (SDOF) Systems: Understanding free and forced vibrations. While you might be looking for a free

• The equation of motion for a single-degree-of-freedom system: $$m \fracd^2xdt^2 + c \fracdxdt + kx = F_0 \sin(\omega t)$$
• The natural frequency of a single-degree-of-freedom system: $$\omega_n = \sqrt\frackm$$
• The damping ratio of a single-degree-of-freedom system: $$\zeta = \fracc2 \sqrtkm$$