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
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