Sujet Grand Oral Maths Physique Site

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.

Because every time the wind blows through the new vault, it doesn't whisper a prayer. It whispers a second-order differential equation. Sujet Grand Oral Maths Physique

It seemed so abstract. So dead. Little did I know that this equation would become the heartbeat of a cathedral. The fire changed everything. The natural frequency of the vault’s oscillatory mode

[ 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 ] It seemed so abstract

Then I lit a small alcohol burner under my scale model. A steel ball hung from a spring—a simple oscillator. Without damping, it swung wildly. Then I dipped the spring in a jar of honey (my analog for the polymer). The motion stopped. Dead.