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
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude of oscillation analyze approximation Assume birth c₁ calculation characteristics Consider constant coefficient corresponding d2x dt2 damping de/dt decreases delay depend derived determine difference equation discussed dx dt dx/dt energy integral equilibrium population equilibrium solution equivalent example exercise exponential Figure formula function growth rate Hint increases initial conditions initial value problem isoclines linearized stability analysis logistic equation mass mathematical model maximum method of characteristics motion moving N₁ Newton's nonlinear pendulum number of cars obtained occur ordinary differential equations oscillation P₁ partial differential equation period phase plane Pmax population growth potential energy r₁ result sharks shock Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solution curves solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow trajectories Umax unstable equilibrium position variables vector x₁ yields zero