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A oscillating wave-energy-converter (WEC) can be modelled as a mass-spring system forced by sinusoidal waves. A...

A oscillating wave-energy-converter (WEC) can be modelled as a mass-spring system forced by sinusoidal waves. A simple model would be given by the following DE:

x''(t) + x'(t) + Kx(t) = h sin(ωt),

where x measures the position of the WEC; K is a tuning parameter, chosen so that the WEC resonates with the waves; h is the height of the waves; and ω is the frequency of the waves. (a) Find a particular solution for the model.

(b) Using your answer in (a), find the value of k that makes the amplitude of the oscillations the largest AND the value of the maximum amplitude.

(c) Which frequency waves will give the largest amplitude oscillations?

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