In the overdamped regime, the general solution becomes:
[ m\ddot{x} + c\dot{x} + kx = F_0 \cos(\omega_f t) ]
I solved the characteristic equation. I calculated the discriminant. I showed them the Fourier transform of the fire’s temperature.
I shouted at my screen. My mother ran in. "Léa? What is it?"
I left his office humiliated. That night, I opened my math textbook to the chapter on —specifically, the harmonic oscillator and its general form:
I grinned. That was the final test.