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Sujet Grand Oral Maths Physique Apr 2026

[ m\ddot{x} + c\dot{x} + kx = F_0 \cos(\omega_f t) ]

In the overdamped regime, the general solution becomes: Sujet Grand Oral Maths Physique

I solved the homogeneous equation first: (x_h(t) = A e^{r_1 t} + B e^{r_2 t}), where (r_1) and (r_2) are roots of the characteristic equation (mr^2 + cr + k = 0). [ m\ddot{x} + c\dot{x} + kx = F_0

"Léa, what is the link between your mathematics and physics specialities?" Sujet Grand Oral Maths Physique

I shouted at my screen. My mother ran in. "Léa? What is it?"

[ x_p(t) = \frac{1}{m\omega_d} \int_0^t F_{\text{thermal}}(\tau) e^{-\frac{c}{2m}(t-\tau)} \sin(\omega_d (t-\tau)) d\tau ]

I took a breath. I told them the story of the fire. Not as a tragedy—but as a differential equation.