Question

 Mathematical modelling of mechanical systems is crucial to problem-solving. Support the statement by communicating your understanding of modelling within this context. 

Answer 1

A good design can save a lot of time and money effort when you start to test and deploy your system in the real world; it might take more time pondering over the right design before you actually implement it; in the long term, it is worth of modeling as it helps you avoid unnecessary debugging and keep your system away from exposing obvious bugs, more importantly, it can help you find implicit bugs easily if you have a good design blueprint and save a lot of maintenance effort in future.

Given all those benefits of a good design, a natural question is how I can make a good design for my desired mechanical system? (The same question can be raised for other critical controlling systems too.) The answer is a mathematical model! It’s the primary tool you can use to rigorously reason/prove about your system before you actually heading to implement it. When the system is complex and big, it is also critical, like flight control, medical devices, etc.; it is a good mindset to have a mathematical model before head.

Recently, there is active research in developing mathematical modeling tools that help people from various fields design their systems. If you are interested, you can check out this tool.

Applications:

Often when engineers analyze a system to be controlled or optimized, they use a mathematical model. In analysis, engineers can build a descriptive model of the system as a hypothesis of how the system could work or estimate how an unforeseeable event could affect the system. Similarly, in control of a system, engineers can try out different control approaches in simulations.

A mathematical model usually describes a system by a set of variables and equations that establish relationships between the variables. Variables may be of many types; real or integer numbers, boolean values, or strings, for example. The variables represent some properties of the system; for example, the measured system often outputs signals, timing data, counters, and event occurrence (yes/no). The actual model is the set of functions that describe the relations between the different variables.