Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 25
... simple expression for the motion of the center of mass is quite interesting , but hardly aids in understanding the possibly complex behavior of each individual mass . Try subtracting equation 9.2 from equation 9.1 ; you will soon ...
... simple expression for the motion of the center of mass is quite interesting , but hardly aids in understanding the possibly complex behavior of each individual mass . Try subtracting equation 9.2 from equation 9.1 ; you will soon ...
Page 154
... simple model of the population growth of a species limited by the food supply based on experiments on a type of water bug . As in the logistic model , the growth rate is proportional to the difference between the available food f , and ...
... simple model of the population growth of a species limited by the food supply based on experiments on a type of water bug . As in the logistic model , the growth rate is proportional to the difference between the available food f , and ...
Page 331
... simple experiment to measure the maximum flow . Position an observer at a traffic light . Wait until the light turns ... simple velocity - density relationship having the general desired features . Hopefully enough qualitative insight ...
... simple experiment to measure the maximum flow . Position an observer at a traffic light . Wait until the light turns ... simple velocity - density relationship having the general desired features . Hopefully enough qualitative insight ...
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