The exercise involves an electrical circuit with a capacitor $C$, an inductor $L$, and a resistor $r$. The setup indicates a situation where the capacitor is charged and an interrupt switch (K) is activated to begin oscillations, leading to a variation in the capacitor's charge over time.

Let's break down the tasks from the exercise:

1. Determine the differential equation verified by the charge $q(t)$:

   • Based on the circuit, we can expect this to involve an LC circuit with a capacitor, inductor, and potentially a resistor. The oscillatory nature indicates a second-order linear differential equation, commonly written as: $L \frac{d^2q}{dt^2} + r \frac{dq}{dt} + \frac{q}{C} = 0$ The resistive term (due to $r$) is small, so it might be negligible in the case you're analyzing.

2. Identify the regime of oscillations:

   • Based on the oscillatory nature of $q(t)$, it appears this could be an underdamped regime, where oscillations are present but slowly decay over time.

3. Determine the pseudo-period $T$:

   • The pseudo-period is the period of the oscillation, which can be found using the graph provided. It corresponds to the time between two peaks of the oscillation.

4. Calculate the energy dissipated by Joule effect between the instants $t_1 = 0.006 \, s$ and $t_2 = 0.03 \, s$:

   • Energy dissipated can be calculated from the power dissipated in the resistor $P = r I^2$, where $I$ is the current. However, for simplification, the graph and the small resistance assumption may allow for approximations.

Do you want help working through each of these parts step by step, or do you have specific questions on a particular one? Let me know!