Unformatted text preview: b. Find the Lagrangian and the equations of motion (15 pts). 4. (20 pts) Fourier series. A damped harmonic oscillator is described by the equation ) ( 2 2 t f x x x = + + ω β , where ) ( t f is a periodic function with period τ , and for < < t , = t t f π 2 sin ) ( . a. Sketch ) ( t f , and expand ) ( t f in Fourier series. (6 pts) b. Find the particular solution ) ( t x p , or rather, the Fourier series of it. (4 pts) c. Set 1 . = , 1 = , 1 = . Use a computer program to plot the 4 leading terms (including the constant term) of ) ( t f and ) ( t x p . (5 pts) M m 2 m 1 m g l g R...
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 Spring '09
 R
 Equations, Fourier Series, Periodic function, pts

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