Transient analysis

Transient analysis, in the context of electrical engineering or systems dynamics, refers to a type of simulation used to analyze how a system's behavior changes over time in response to initial conditions or sudden changes in inputs[^4]. It helps engineers understand how a system evolves from its equilibrium state to reach a new steady-state condition. This method is commonly employed in circuit analysis, mechanical systems, and control systems.

For example, in electrical circuits, transient analysis calculates the voltage and current waveforms when a switch is turned on or off[^5]. The goal is to find the transient response that decays to the steady-state values after a disturbance[^6].

Here's a simple demonstration using Python's `pandas` library for a step function input[^7]:

import numpy as np
import pandas as pd

# Define a simple RC circuit impulse response
def impulse_response(t, R, C):
    return np.exp(-t / (R * C))

# Create a time vector
t = np.linspace(0, 10, 1000)

# Define initial conditions and parameters
R = 100  # Resistance in ohms
C = 1   # Capacitance in farads
V_initial = 0  # Initial voltage

# Perform transient analysis
response = impulse_response(t, R, C) + V_initial

# Plot the transient response
df = pd.DataFrame({'Time': t, 'Response': response})
df.plot(x='Time', y='Response')