Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 38
... maximum displacements is a constant . 12.4 . If c < 0 , the force is called a negative friction force . ( a ) In this case , show that x → ∞ as t - → ∞ . ( b ) If in addition c2 < 4mk , then roughly sketch the solution . 12.5 ...
... maximum displacements is a constant . 12.4 . If c < 0 , the force is called a negative friction force . ( a ) In this case , show that x → ∞ as t - → ∞ . ( b ) If in addition c2 < 4mk , then roughly sketch the solution . 12.5 ...
Page 290
... maximum of the flow occurs at the only local maximum . q = pu ( p ) Flow ρ max p Density Figure 63-2 Fundamental Diagram of Road Traffic ( flow - density curve ) . dq dp 818 Pmax Figure 63-3 . The data from the Lincoln Tunnel indicate a ...
... maximum of the flow occurs at the only local maximum . q = pu ( p ) Flow ρ max p Density Figure 63-2 Fundamental Diagram of Road Traffic ( flow - density curve ) . dq dp 818 Pmax Figure 63-3 . The data from the Lincoln Tunnel indicate a ...
Page 331
... maximum . In the problem just discussed , as soon as the light changes from red to green , the maximum flow occurs at the light , x = stays there for all future time . This suggests a simple experiment to measure the maximum flow ...
... maximum . In the problem just discussed , as soon as the light changes from red to green , the maximum flow occurs at the light , x = stays there for all future time . This suggests a simple experiment to measure the maximum flow ...
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