Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 113
... exercise 28.3 without a restoring force ( i.e. , k = = 0 ) . ( a ) How do you expect the solution to behave ? ( b ) Let v = dx / dt and sketch the solution in the phase plane . ( c ) Let v = dx / dt and solve the problem exactly . ( d ) ...
... exercise 28.3 without a restoring force ( i.e. , k = = 0 ) . ( a ) How do you expect the solution to behave ? ( b ) Let v = dx / dt and sketch the solution in the phase plane . ( c ) Let v = dx / dt and solve the problem exactly . ( d ) ...
Page 143
... exercise 35.5 . 35.7 . Collect human population data in the United States , including the present population and the ... exercise 35.7 to exercise 35.8 . 35.10 . Redo exercise 35.7 without ignoring migration . 35.11 . Redo exercise 35.8 ...
... exercise 35.5 . 35.7 . Collect human population data in the United States , including the present population and the ... exercise 35.7 to exercise 35.8 . 35.10 . Redo exercise 35.7 without ignoring migration . 35.11 . Redo exercise 35.8 ...
Page 151
... exercise 36.4 by an alternative method . ( a ) If you have not already done so , do exercise 36.4a . ( b ) Using the differential equation for Pn . + j ( t ) , show that ( c ) What is E ( 0 ) ? dE dt = · Ε . ( d ) Derive the result of ...
... exercise 36.4 by an alternative method . ( a ) If you have not already done so , do exercise 36.4a . ( b ) Using the differential equation for Pn . + j ( t ) , show that ( c ) What is E ( 0 ) ? dE dt = · Ε . ( d ) Derive the result of ...
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