Sujet Grand Oral Maths Physique Info

[ x(t) = e^{-\frac{c}{2m}t} \left( A \cos(\omega_d t) + B \sin(\omega_d t) \right) + X \cos(\omega_f t - \phi) ]

I wrote on the board:

This is the story of how I used a second-order differential equation to prove that the impossible could be rebuilt. Three weeks before the fire, I had failed my mock physics exam. My teacher, Monsieur Delacroix, had drawn a simple arch on the blackboard. "Explain the stability of the Romanesque vault," he said.

It seemed so abstract. So dead. Little did I know that this equation would become the heartbeat of a cathedral. The fire changed everything. Sujet Grand Oral Maths Physique

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

To rebuild Notre-Dame, they would not need stronger stone. They would need . My proposal: inject a viscoelastic polymer (a modern physics material) into the ancient joints. This would raise (c) by a factor of 10, pushing the system from underdamped ((\Delta < 0)) to overdamped ((\Delta > 0)).

I grinned. That was the final test.

The fire didn’t burn the spire down. The fire shook the spire apart. The vibrations from the thermal pulses amplified until the amplitude went to infinity in theory—but in reality, until the mortar turned to dust and the keystone slipped.

And today, as they rebuild Notre-Dame, they are indeed injecting a modern polymer into the ancient mortar. They didn't get the idea from me—but in my heart, I know the math was right.

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(t) = e^{-\frac{c}{2m}t} \left( A \cos(\omega_d t)

I wrote:

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.