hw6 - March 5, 2010 Cornell University, Department of...

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Unformatted text preview: March 5, 2010 Cornell University, Department of Physics P3318, Analytical Mechanics, HW#6, due: 3/12/10, 2:30PM (at section) Question 1 : Validity of small oscillations Consider a particle of mass m in a one dimensional potential of the form V ( x ) = log bracketleftbigg cosh parenleftbigg x- x d parenrightbiggbracketrightbigg . (1) 1. What are the dimensions of , x and d ? 2. Where is the minimum of that potential? Rewrite it using a coordinate that vanish in the minimum. 3. Assume that the oscillations are small and expand the potential such that you get a harmonic potential. Then, solve the problem in this approximation, that is, find the frequency of the oscillations. 4. Identify the condition when the oscillations can be treated as small. Write your answer in terms of the parameters of the problem and the energy. Question 2 : Two pendulums with a spring (This is basically section 9.1 in Hand and Finch.) Consider two pendulums with a spring between them. Calculate the normal modes of this system assuming small oscillations. Whatbetween them....
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This note was uploaded on 03/29/2010 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell University (Engineering School).

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hw6 - March 5, 2010 Cornell University, Department of...

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