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 |
NEWTONS LAW 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
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