1. 1st order examples: A good test of understanding is to ask how these concepts and analogies might be extended and/or applied to each engineering discipline.
Mixing tank,   House temperature,   Mass-damper,   tank level,   pain relief,   thermal system,   electrical system,   heat exchanger,   dcservo,   savings and debt models.
2. 2nd order examples:
It is noted that many examples are electro-mechanical and thus are relevant across all engineering disciplines.
Mass-spring-damper,   Diabetes,   dc servo,   car velocity,  , house temperature,   tank level,   aeroplane roll,   pulleys and gears,   electrical circuits,
3. Collations, analogies and comparisons: An interesting coursework would be to form some collations of your own, relevant to your own studies.
Biology examples,   heat exchanger examples,   mixing examples.
4. Impact of feedback and under-damping: A lot of real-life examples lead to over-damped 2nd order models. However, the necessary introduction of feedback often makes these become under-damped.
Cruise control,   heat exchanger examples,   DC servo.