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Unformatted text preview: Phys. 7268 Assignment 4 Due: 2/24/11 Problem 1 Identification of a Dimensionless Stress Parameter. To see how a dimensionless stress parameter like the Rayleigh number might be discovered from known dynamical equations, consider the evolution equation for a damped driven pendulum, m + + C sin( ) = A sin( t ) , (1) where m is the mass of the pendulum, ( t ) is the angle of the pendulum with respect to the vertical (so = 0 means the particle hangs down vertically underneath the fulcrum), is the damping coefficient, A is the amplitude of the external driving, is the frequency of the external driving, and overhead dots denotes differentiation with respect to time, e.g., = d 2 /dt 2 . One parameter in this equation can be eliminated immediately by dividing both sides of Eq. (1) by m , which redefines m = 1 and the other parameters to the values /m , C/m , and A/m . A second parameter can be eliminated by defining a new dimensionless time coordinate t by the transformation: t = c t t, where c t is a new unit of time. (a) Write down Eq. (1) in the new variable t by substituting and using the chain rule of calculus....
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This note was uploaded on 08/25/2011 for the course PHYS 7268 taught by Professor Staff during the Spring '11 term at Georgia Institute of Technology.
- Spring '11