Dynamic Signals — Introduction and Learning Goals

Dynamic Signals — Introduction and Learning Goals#

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.

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