As you have seen in previous chapters, RLC circuits are fundamental in electrical engineering for modeling transient and steady-state behaviors in response to various inputs. In a series RLC circuit, the resistor (R), inductor (L), and capacitor (C) are connected in series, and their combined response to an applied voltage can be described by a second-order differential equation. When a step input voltage is applied, the resulting voltage across the capacitor exhibits characteristic transient behavior, which can be underdamped, critically damped, or overdamped depending on the circuit parameters.

Numerical simulation using Python's scipy.integrate.odeint allows you to solve such differential equations efficiently, providing insight into how the circuit responds over time. By simulating the voltage across the capacitor, you can visualize and analyze the damping behavior, which is crucial for understanding and designing real-world circuits.