The step response of second-order oscillator systems is given by the following equation:

where is the time, (Greek letter "xi") is the damping ratio, and (Greek letter "omega") is the undamped natural frequency.

The following figure is a 2-by-1 subplot. The top subplot contains a plot of against for various values. The bottom subplot contains a plot of  against for a single value of  and the maximum value is marked.

Write the Python code to reproduce the figure, using the following information:

• Any required packages must be imported
• A lambda function must be used to define y
• = 10.26
• is a 1D array from 0 to 1 (inclusive) with 200 points
• The line colour specifications are Python's default and do not need to be explicitly stated
• The titles and axes are labelled accordingly
• The figure layout is constrained

• Top subplot:

  • = 0.2, 0.4, 0.6, 0.8

  • The legend should not be hardcoded and is positioned in the best location
  • A loop should be used

• Bottom subplot:

  • = 0.65
  • The maximum point is marked with a red diamond
  • The grid is turned on
  • The legend should not be hardcoded and is positioned in the lower right corner

Copy and paste your Python code in the plain text box below.

The following file contains rainfall rate (mm/hr) throughout a day, recorded at each hour. The first value in the data file corresponds to 00:00 hours (24-hour clock). The last entry is at 23:00.

Download the file here (you must access this using your Monash login. If the "save as" dialogue box does not appear when you click on the link, save the file by right-clicking on the link and then selecting "save link as...").

Find the total rainfall using all the given points using the composite trapezoidal rule, correct to at least 1 decimal place.

All cell formulae must reference cells in the same sheet

How should you include a parameter or fixed variable in a cell operation or function?

When is it preferable to use a program or script instead of an Excel spreadsheet?

Which of the following best describes your responsibility when using GenAI-generated code in a project?

Which of the following tasks is generative AI currently best at?