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Unformatted text preview: Ph507. Homework 8 (due: Monday, April 11).PROBLEM 81 (4 pts)Two identical oscillators are placed in viscous medium. They are coupled due to dissipative hydrodynamic interactions (γterms in the equations of motion below). One of the oscillator is subjected to periodic driving force,fei't.:¨x+δ˙x+'2x=γ˙y+fmei't;¨y+δ˙y+'2y=γ˙x.Find the amplitude of oscillations of the other oscillator (i.e. amplitude ofy).PROBLEM 82 (6 pts)Find thefxed points, analyze their stability and sketch the phase space behavior for the following systems:a) A dynamical system with the following equations of motion (consider all possible topologies of the phase space"portrait"):˙x=−¡x2+y2+a−1¢y˙y=¡x2+y2+a+ 1¢xb) A pendulum with dumpingδsubjected to constant torqueτ:˙pθ=τ−I'2sinθ−δpθ;˙θ=pθI.PROBLEM 83 (5 pts)a) Find the canonical transformation(q, p)−→(Q, P), upon which one of the new variables has the form of enegryof a linear oscillator:Q(q, p) =p22m+kq22b) Consider a system of two coupled oscillators:...
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This note was uploaded on 09/28/2008 for the course PHYS 507 taught by Professor Anon during the Spring '04 term at Cornell University (Engineering School).
 Spring '04
 ANON
 mechanics, Work

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