Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 21
... initial value problem the mass is initially at rest . Two initial conditions are necessary since the differential equation involves the second derivative in time . To solve this initial value problem , the arbitrary constants c1 and c2 ...
... initial value problem the mass is initially at rest . Two initial conditions are necessary since the differential equation involves the second derivative in time . To solve this initial value problem , the arbitrary constants c1 and c2 ...
Page 42
... initial conditions can be satisfied . Show that this solution does not approximate very well the solution to ( a ) for all time . 13.5 . Assume that c2 > 4mk . ( a ) Solve the initial value problem , that is , at t = 0 , x = ( b ) Take ...
... initial conditions can be satisfied . Show that this solution does not approximate very well the solution to ( a ) for all time . 13.5 . Assume that c2 > 4mk . ( a ) Solve the initial value problem , that is , at t = 0 , x = ( b ) Take ...
Page 146
... initial conditions are necessary . These are the initial probabilities . The problem we will solve is one in which the initial population ( t = 0 ) is known with certainty , being some value No. In that case all the initial ...
... initial conditions are necessary . These are the initial probabilities . The problem we will solve is one in which the initial population ( t = 0 ) is known with certainty , being some value No. In that case all the initial ...
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