Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 17
... equivalent length in feet or miles and the equivalent mass in pounds will appear afterwards in parentheses . What is the dimension of dx / dt , the velocity ? Clearly , dx L dt = a length L divided by a time T. Mathematically we note ...
... equivalent length in feet or miles and the equivalent mass in pounds will appear afterwards in parentheses . What is the dimension of dx / dt , the velocity ? Clearly , dx L dt = a length L divided by a time T. Mathematically we note ...
Page 186
... equivalent to another , namely + is equivalent to + , yielding three distinct types of interactions . If both populations enhance the other ( ++ ) , then the biological interaction is called mutualism or symbiosis . If both populations ...
... equivalent to another , namely + is equivalent to + , yielding three distinct types of interactions . If both populations enhance the other ( ++ ) , then the biological interaction is called mutualism or symbiosis . If both populations ...
Page 375
... equivalent to equation 82.5 . The line of cars dissipates at time ta , when ( see Fig . 82-5 ) Umax Pota Pmax - umaxt Umaxtd T ) . Hence , ta max ( 1 ( 1 - Po Po 1 Pmax Pmax ( 82.6 ) The time it takes to dissipate the line after the ...
... equivalent to equation 82.5 . The line of cars dissipates at time ta , when ( see Fig . 82-5 ) Umax Pota Pmax - umaxt Umaxtd T ) . Hence , ta max ( 1 ( 1 - Po Po 1 Pmax Pmax ( 82.6 ) The time it takes to dissipate the line after the ...
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