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 $\zeta =e^{-i\phi }w{e}^{-w}$ with $w=\beta t+i\Omega t$, which transforms the dynamics into a logarithmic spiral. Within…