Right Circular Cone with Height, Radius and Frustum FormulaRight Circular Cone (Volume) $$ V ~=~ \frac{\pi}{3} \, h \, r^2 $$
Parallel Shifted Axis of Rotation of a Cylinder FormulaSteiner's Theorem (Moment of Inertia) $$ I ~=~ I_{\text{CM}} ~+~ \class{brown}{m} \, h^2 $$
Amplitude-Frequency Graph of a Forced Damped Oscillator FormulaSinusoidally Forced Damped Oscillator (Amplitude) $$ A_0 ~=~ \frac{F_0}{ m \sqrt{ (\omega^2 - {\omega_0}^2)^2 ~+~ \frac{b^2\,\omega^2}{m^2}}} $$
Amplitude-Frequency Graph of a Forced Damped Oscillator FormulaSinusoidally Forced, Damped Oscillator (Phase Angle) $$ \varphi_0 ~=~ \arctan\left( \frac{\omega_0^2 - \omega^2}{\omega \, b} \, m \right) $$
Hooke Law: Displacement of the spring and restoring force FormulaDamped Harmonic Oscillator (Frequency, Damping Constant) $$ f ~=~ \frac{1}{2\pi} \sqrt{\frac{D}{m} ~-~ \frac{b^2}{4m^2}} $$
Hooke Law: Displacement of the spring and restoring force FormulaHarmonic Oscillator (Velocity-Position Function) $$ v(x) ~=~ \sqrt{ \frac{D}{m} \, \left(A^2 - x^2\right) } $$
Hooke Law: Displacement of the spring and restoring force FormulaHarmonic Oscillator (Maximum Acceleration) $$ a_{\text{max}} ~=~ \frac{D}{m}\,A $$
Hooke Law: Displacement of the spring and restoring force FormulaHarmonic Oscillator (Maximum Velocity) $$ v_{\text{max}} ~=~ \sqrt{ \frac{D}{m} } \, A $$