\begin{equation} f = \frac{1}{T} \quad T = \frac{1}{f} \qquad (\textnormal{Relationship between frequency and period}) \tag{1} \end{equation} \begin{equation} \omega = 2 \pi f = \frac{2 \pi}{T} \qquad (\textnormal{Angular frequency}) \tag{2} \end{equation} \begin{equation} F_x = - k x \qquad (\textnormal{Restoring force by an ideal spring}) \tag{3} \end{equation} \begin{equation} a_x = \frac{d^2 x}{dt^2} = - \frac{k}{m} x(t) \qquad (\textnormal{Simple harmonic motion}) \tag{4} \end{equation} \begin{equation} \omega = \sqrt{ \frac{k}{m} } \qquad (\textnormal{Angular frequency SHM}) \tag{5} \end{equation} \begin{equation} f = \frac{\omega}{2 \pi} = \frac{1}{2 \pi} \sqrt{\frac{k}{m}} \qquad (\textnormal{Cyclical frequency SHM}) \tag{6} \end{equation} \begin{equation} T = \frac{1}{f} = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{m}{k}} \qquad (\textnormal{Period SHM}) \tag{7} \end{equation} \begin{equation} x(t) = A \, \textnormal{cos} (\omega t + \phi) \qquad (\textnormal{Displacement SHM}) \tag{8} \end{equation} \begin{equation} E = \frac{1}{2} m v_x^2 + \frac{1}{2} k x^2 = \frac{1}{2} k A^2 = C \qquad (\textnormal{Total mechanical energy SHM}) \tag{9} \end{equation} \begin{equation} \omega = \sqrt{\frac{\kappa}{I}} \quad f = \frac{1}{2 \pi} \sqrt{\frac{\kappa}{I}} \qquad (\textnormal{Angular SHM}, \kappa = \textnormal{torsion constant}) \tag{10} \end{equation} \begin{equation} \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{mg/L}{m}} = \sqrt{\frac{g}{L}} \qquad (\textnormal{Simple pendulum, small displacement}) \tag{11} \end{equation} \begin{equation} f = \frac{\omega}{2 \pi} = \frac{1}{2 \pi} \sqrt{\frac{g}{L}} \qquad (\textnormal{Cyclical frequency, simple pend., small amplitude }) \tag{12} \end{equation} \begin{equation} T = \frac{2 \pi}{\omega} = \frac{1}{f} = 2 \pi \sqrt{\frac{L}{g}} \qquad (\textnormal{Period, simple pend., small amplitude }) \tag{13} \end{equation} \begin{equation} \omega = \sqrt{ \frac{mgd}{I}} \qquad (\textnormal{Angular frequency, physical pendulum, small amplitude }) \tag{14} \end{equation} \begin{equation} T = 2 \pi \sqrt{ \frac{I}{mgd}} \qquad (\textnormal{Physical pendulum, small amplitude }) \tag{15} \end{equation} \begin{equation} x(t) = A \, e^{- (b/2m)t} \textnormal{cos}(\omega t + \phi) \qquad (\textnormal{Oscillator with small damping }) \tag{16} \end{equation} \begin{equation} \omega = \sqrt{ \frac{k}{m} - \frac{b^2}{4m^2}} \qquad (\textnormal{Angular frequency, oscillator small amplitude }) \tag{17} \end{equation} \begin{equation} A = \frac{F_{max}}{ \sqrt{(k - m \omega_d^2)^2} + b^2 \omega_d^2 } \qquad (\textnormal{Amplitude of driven oscillator, d = driver }) \tag{18} \end{equation}
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