Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 14
... expression for tan do , and using sin2 + cos2 0 1 results in an equation for A2 : = A = ( c + c ) 1/2 Фо = tan - 1 C1 . C2 The expression , x = A sin ( wt + po ) , is especially convenient for sketching the displacement as a function of ...
... expression for tan do , and using sin2 + cos2 0 1 results in an equation for A2 : = A = ( c + c ) 1/2 Фо = tan - 1 C1 . C2 The expression , x = A sin ( wt + po ) , is especially convenient for sketching the displacement as a function of ...
Page 66
... expression for conservation of energy , evaluate the maximum displacement of the mass from its equilibrium position . Compare this to the result obtained from the exact explicit solution . ( d ) What is the velocity of the mass when it ...
... expression for conservation of energy , evaluate the maximum displacement of the mass from its equilibrium position . Compare this to the result obtained from the exact explicit solution . ( d ) What is the velocity of the mass when it ...
Page 353
... expression as much as possible . ) Show that the shock velocity is the average of the density wave velocities associated with Po and P1 . 77.2 . If u = Umax ( 1 - p2 / Pmax ) , then what is the velocity of a traffic shock separating ...
... expression as much as possible . ) Show that the shock velocity is the average of the density wave velocities associated with Po and P1 . 77.2 . If u = Umax ( 1 - p2 / Pmax ) , then what is the velocity of a traffic shock separating ...
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 |
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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