1. Over damped systems:
Over damped 2nd order systems have two stable real poles. So called because a mass-spring-damper system with a large damping leads to this scenario.
i. Over damped systems.
ii. Very over damped systems.
iii. A talk through video on youtube
iv. Video on very over-damped.
2. Under damped systems:
Under damped essentially means the system will oscillate to some extent. This is an introductory note giving a basic solution method, but without exploiting normalised forms.
i. Under damped response solution.
ii. Talk through video on youtube.
3. Laplace transforms:
Using Laplace methods to solve both over and under damped systems, without normalised forms.
i. Laplace and over damped solution.
ii. Laplace and under damped solution.
iii. Video on overdamped with Laplace.
iv. Video on underdamped with Laplace.
4. Normalised forms:
Gives definition of a normalised form for a 2nd order system in terms of damping ratio and natural frequency. Shows how solutions are characterised in terms of the normalised parameters.
i. Normalised form definition.
ii. Overshoot and decay rate.
iii. Video on normalised forms.
iv. Video on oscillation and overshoot.
5. Analysis and sketching with normalised forms:
Normalised forms give useful insight and generalisations that facilitate quick sketching and characterisation of behaviour.
i. Steady-state behaviour.
ii. Convergence rate dependence on damping.
iv. Video on steady-states.
v. Video on speed of response.
vi. Video on sketching.
6. Using MATLAB:
Gives a quick overview of using dsolve.m in MATLAB code to solve higher order models. Coding requirements are typically only 2-3 lines.
i. Use of MATLAB for higher order systems.
ii. Using Laplace transforms and MATLAB.