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# HW3 - b Find the Lagrangian and the equations of motion(15...

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Physics 110, Problem set #3 Due April 21, 2010 1. (15 pts) Consider example 7.8 in Thornton (p.247). Include the masses of the pulleys ( 2 1 , M M , radii 2 1 , R R ). Find the Lagrangian and equations of motion (10 pts). Find the simple but important integral of the motion (conserved quantity) of the system. (5 pts) 2. (25 pts) This is a tricky problem. Consider the system of a pulley (radius R ), masses 2 1 , m m and a string (length l ) shown in the figure. Ignore the mass of the string and the pulley. a. Find three generalized coordinates to describe the system (5 pts). b. Find the Lagrangian and the equations of motion (20 pts). 3. (20 pts) Consider a rail/mass system as shown. Both the rail and the mass slip downward without friction. a. Find two generalized coordinates to describe the system (5 pts).
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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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