Linear System Response & Analysis - Second Order System Responses

An introduction to the step response of a 2nd order system with complex poles and zero initial conditions using Laplace techniques. Includes illustrations on numerical examples.

Tutorial on the computation of responses for under damped 2nd order systems, using Laplace and time domain methods. Includes worked solutions.

Beginning from the standard form for 2nd order models using damping ratio and natural frequency, considers how the frequency of oscillation and overshoot depend upon the damping ratio (assumed less than one). Uses zero initial conditions.

Beginning from the standard form for 2nd order models using damping ratio and natural frequency, gives questions on simple and quick analytic computations can be used to produce an accurate sketch of the step response (for zero initial conditions).Includes worked solutions.

Tutorial questions on the computation of step responses, for zero initial condition, for over damped 2nd order systems. Uses time domain and Laplace methods. Includes a few examples on the use of approximation for very over damped systems. Includes worked solutions.

Questions on the standard form for 2nd order models and thus definitions of damping ratio and natural frequency. Uses ODEs and Laplace transforms. Includes worked solutions.

Beginning from the standard form for 2nd order models using damping ratio and natural frequency, shows how some simple and quick analytic computations can be used to produce an accurate sketch of the step response (for zero initial conditions).

Beginning from the standard form for 2nd order models using damping ratio and natural frequency, how does the speed of covergence depend upon the damping ratio? Includes numerical examples showing how to compute the speed of response and thus illustrate the key insights.

Define the standard form for 2nd order models using damping ratio and natural frequency. Includes numerical examples showing how to compute the key characteristics.

Repeats the solutions of the first two videos, that is step responses of 2nd order systems with real poles, but this time using Laplace transform techniques rather than the time domain. Illustrates with numerical examples.

An introduction to the step response of a 2nd order system with two real poles. Derives an analytic solution assuming zero initial conditions and illustrates on numerical examples. Solutions tackled in the time domain.

Using the standard form for 2nd order models, what impact do the parameters and in particular the damping ratio have on the steady-state gain? Assume stable models only.

An introduction to the step response of a 2nd order system with complex poles and zero initial conditions. Derives solutions from first principles in the time domain and illustrates on numerical examples.

Adds insight to the 1st video on step responses of a 2nd order system with two real poles. This video considers the repercussions of the poles being widely spaced and illustrates with numerical examples. Solutions tackled in the time domain.