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Transient & Fourier Waveforms

See attached Worksheet. Explanation also required as I am trying to solve these by myself also.

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Solution Summary

From a set of initial conditions such as given angular frequencies and damping constants second order responses are derived using Excel and paperwork theory. Further a periodic waveform is defined in the time domain and its Fourier series components are derived using Fourier series theory. An Excel spreadsheet is used as a modelling toll to derive constants