Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 31
... friction between a spring - mass system and a table , illustrated in Fig . 10-5 , does not act in the way previously described , F1 - c ( dx / dt ) . Instead , experiments ... friction . However , in this text for the 31 Sec . 10 Friction.
... friction between a spring - mass system and a table , illustrated in Fig . 10-5 , does not act in the way previously described , F1 - c ( dx / dt ) . Instead , experiments ... friction . However , in this text for the 31 Sec . 10 Friction.
Page 32
... friction . However , in this text for the most part , we will limit our discussion to linear damping , Ff = -c dx dt EXERCISES 10.1 . Suppose that an experimentally observed frictional force is approximated by Ff = α ( dx / dt ) 3 ...
... friction . However , in this text for the most part , we will limit our discussion to linear damping , Ff = -c dx dt EXERCISES 10.1 . Suppose that an experimentally observed frictional force is approximated by Ff = α ( dx / dt ) 3 ...
Page 36
... friction . However , the mass never absolutely stops . As long as there is friction ( c > 0 ) , no matter how small , it cannot be ignored as the amplitude of the oscillation will diminish in time only with friction . In this case ...
... friction . However , the mass never absolutely stops . As long as there is friction ( c > 0 ) , no matter how small , it cannot be ignored as the amplitude of the oscillation will diminish in time only with friction . In this case ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero