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 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero