Short summary Time-domain and dynamical-system behavior: step responses, first/second order systems, and vibration-based measurements.
Learning objectives
Interpret first- and second-order system responses and key parameters (time constant, damping, natural frequency).
Extract physical quantities (e.g., mass from vibrations) from measured signals.
Link time-domain responses to frequency content.
Key concepts (brief)
Step response, log-decrement, and damping ratio estimation.
Modal interpretation for simple systems and measurement-driven parameter estimation.
Practical considerations: sensor dynamics and filtering.
Recommended notebooks to run
first_order_time_response.ipynb
step_response.ipynb
2nd_order_system_step_function_log_decrement.ipynb
mass_measurement_using_vibrations.ipynb
design_choice_2nd_order_pressure_transducer.ipynb
Suggested exercises
Estimate time constant and uncertainty from a noisy step response.
Use a recorded vibration signal to estimate a lumped mass or natural frequency.
Prerequisites Ordinary differential equations basics and elementary signal processing.