Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 308
... wave velocity can thus be positive or negative ! In the next section we will attempt to describe what a density wave is , in particular , what it means for the velocity of a density wave to be negative ! 67.1 . Suppose that q Road ...
... wave velocity can thus be positive or negative ! In the next section we will attempt to describe what a density wave is , in particular , what it means for the velocity of a density wave to be negative ! 67.1 . Suppose that q Road ...
Page 312
... Wave on a " jumping " rope . When the rope is vertically moved by the person illustrated above , a “ dis- turbance " is propagated at first to the right . A wave appears to move to the right , but we all know that the particles of the ...
... Wave on a " jumping " rope . When the rope is vertically moved by the person illustrated above , a “ dis- turbance " is propagated at first to the right . A wave appears to move to the right , but we all know that the particles of the ...
Page 349
... wave or simply a shock , † occurs at x , ( t ) , called the position of the shock . Let both the * A function f ( x ) ... wave , is introduced because of the analogous behavior which occurs in gas dynamics . There , changes in pressure and ...
... wave or simply a shock , † occurs at x , ( t ) , called the position of the shock . Let both the * A function f ( x ) ... wave , is introduced because of the analogous behavior which occurs in gas dynamics . There , changes in pressure and ...
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