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 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др