Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 19
... problem we should compare as much as possible our intuition about what should happen with what the formula predicts . If the two agree , then we expect that our formula gives us the quantitative effects for the given problem - one of ...
... problem we should compare as much as possible our intuition about what should happen with what the formula predicts . If the two agree , then we expect that our formula gives us the quantitative effects for the given problem - one of ...
Page 20
... problem are necessary . Perhaps the intuition is incorrect , in which case the mathematical formulation and solution has aided in directly improving one's qualitative ... problem the 20 Mechanical Vibrations INITIAL VALUE PROBLEM.
... problem are necessary . Perhaps the intuition is incorrect , in which case the mathematical formulation and solution has aided in directly improving one's qualitative ... problem the 20 Mechanical Vibrations INITIAL VALUE PROBLEM.
Page 21
... 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 are determined ...
... 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 are determined ...
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