Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 162
... manner similar to the decaying oscillation of a spring - mass system with fric- tion . Other experiments show wild oscillation as in Fig . 40-1b . The preceding types of experiments motivate us to develop other models of population ...
... manner similar to the decaying oscillation of a spring - mass system with fric- tion . Other experiments show wild oscillation as in Fig . 40-1b . The preceding types of experiments motivate us to develop other models of population ...
Page 163
... manner around a stable equilibrium population . Other types of models will be introduced which may allow oscillations of the observed type . Let us describe one situation in which a population may oscillate about its carrying capacity ...
... manner around a stable equilibrium population . Other types of models will be introduced which may allow oscillations of the observed type . Let us describe one situation in which a population may oscillate about its carrying capacity ...
Page 287
... manner an average density for cars moving at 15 miles per hour can be calculated . Generally the data indicates that increasing the traffic density results in lower car velocities ( although there is an exception in the data ) . The ...
... manner an average density for cars moving at 15 miles per hour can be calculated . Generally the data indicates that increasing the traffic density results in lower car velocities ( although there is an exception in the data ) . The ...
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