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Unformatted text preview: a = 2 and a =-2. b) Sketch the phase portraits of the system for the cases a = 2 and a =-2. c) Indicate stable and instable equilibrium points and the seperatrices in these phase por-traits if they exist. Annotate the seperatices with the energies they correspond to. 1 6. Fourier expansion 12 points We want to consider the periodic driving force F ( t ) = -1 t ∈ i 2 π ω n-π ω , 2 π ω n h for some integer n +1 t ∈ i 2 π ω n, 2 π ω n + π ω h for some integer n . To this end we have to Fnd the ±ourier expansion of this function. a) Sketch F ( t ). b) Obtain the ±ourier expansion F ( t ) = 1 2 a + ∞ X n =1 ( a n cos nωt + b n sin nωt ) of F ( t ). c) Plot the sums of the Frst two terms, Frst three terms, and Frst four terms in the interval [-2 π/ω, 2 π/ω ] for ω = 1rad /s . 2...
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This note was uploaded on 07/17/2008 for the course PHYS 664 taught by Professor Bundschuh during the Fall '04 term at Ohio State.
- Fall '04