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 |
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