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A mass on a spring is subjected to an external force that looks like a triangular...

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Advance Math

A mass on a spring is subjected to an external force that lookslike a triangular wave:

F(t) = 1+t from t=-1 to 0

F(t) = 1-t from t=0 to t=1 Periodicity = 2

The differential equation for the position of the mass (usingNewton’s law) ends up being: x’’(t) + 2x’(t) + 101x(t) = F(t)

1. Find the generic homogeneous solution
2. Find the Fourier series of F(t)

3. Find the Fourier series of the particular solution (which isthe total solution after a long time)

4. Plot the first 5 terms of the series

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