Geometric Analysis of the Damped Harmonic Oscillator via the Lambert W Function

Arpan Sharma, Bhargava R. Jogi, Ken Roberts +2

The underdamped harmonic oscillator is analyzed through the complex mapping $\hat{I}\P =e^{-i\ddot{I}†}w{e}^{-w}$ with $w={\hat{I}}^{2}t+i\hat{I}\text{c◯}t$, which transforms the dynamics into a logarithmic spiral. Wi…