Sujet Grand Oral Maths Physique Apr 2026

with (r_1, r_2) real and negative. No oscillations. No resonance. Survival. Three months later, I stood before the jury. Two professors: one in math, one in physics. A whiteboard behind me. A scale model of a Gothic vault in front of me.

In his office, he showed me a photograph of the Beauvais Cathedral choir, which collapsed in 1284. "They built it too high," he said. "They forgot that the force ( F ) on a pillar is not just the weight above it. It is the integral of stress over the surface. They forgot the math."

[ 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 ] Sujet Grand Oral Maths Physique

I left his office humiliated. That night, I opened my math textbook to the chapter on —specifically, the harmonic oscillator and its general form:

In the overdamped regime, the general solution becomes: with (r_1, r_2) real and negative

[ x(t) = A e^{r_1 t} + B e^{r_2 t} ]

I wrote:

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).

Prologue: The Silence of Notre-Dame It is April 16, 2019. The morning after the fire. I am standing on the cobblestones of Paris, watching the last wisps of smoke curl from the charred skeleton of Notre-Dame Cathedral. The world is crying. But I am not crying. I am calculating. Survival

The natural frequency of the vault’s oscillatory mode? Calculated from ( \omega_0 = \sqrt{\frac{k}{m}} ) where (k = \frac{E \cdot A}{L}) (with (E) = Young’s modulus of limestone (50 , \text{GPa}), (A) cross-section, (L) length). It was... 0.499 Hz.