## Harmonic Oscillator (Maximum Velocity)

` $$ v_{\text{max}} ~=~ \sqrt{ \frac{D}{m} } \, A $$ `

Here you will learn the laws of **motion of bodies** (e.g. particles, cars, planets) under the influence of **mechanical forces**. Master the power to predict the future location and state of these bodies - whether the body is particle-like or wave-like.

` $$ v_{\text{max}} ~=~ \sqrt{ \frac{D}{m} } \, A $$ `

` $$ a(t) ~=~ -\omega^2 \, A \, \cos(\omega \, t + \varphi) $$ `

` $$ v(t) ~=~ -\omega \, A \sin(\omega \, t + \varphi) $$ `

` $$ f ~=~ \frac{1}{2\pi} \sqrt{\frac{D}{m}} $$ `

` $$ y(t) ~=~ A \cos(\omega \, t + \varphi) $$ `

` $$ \omega ~=~ 2\pi \, f $$ `

` $$ T ~=~ \frac{1}{f} $$ `

Here you will learn how wavenumber is defined, how it can be calculated and illustrated, and how it is related to angular wavenumber.

` $$ \nu ~=~ \frac{1}{\lambda} $$ `

` $$ k ~=~ 2\pi \, \nu $$ `

` $$ k ~=~ \frac{2\pi}{\lambda} $$ `

` $$ \varphi ~=~ \frac{ \class{red}{s} }{r} $$ `

` $$ Q ~=~ \frac{ \pi \, R^4 \, \left( \mathit{\Pi}_1 ~-~ \mathit{\Pi}_2 \right) }{ 8 \eta \, L } $$ `