Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 4
... motions of clock - like mechanisms and , in a sense , also aid in the understanding of the up - and - down motion of the ocean surface . Physical problems cannot be analyzed by mathematics alone . This should be the first fundamental ...
... motions of clock - like mechanisms and , in a sense , also aid in the understanding of the up - and - down motion of the ocean surface . Physical problems cannot be analyzed by mathematics alone . This should be the first fundamental ...
Page 15
... motion of a spring - mass system . This motion is referred to as simple harmonic motion . The mass oscillates sinusoidally around the equilibrium position x = 0. The solution is periodic in time . As illustrated in Fig . 5-1 , the mass ...
... motion of a spring - mass system . This motion is referred to as simple harmonic motion . The mass oscillates sinusoidally around the equilibrium position x = 0. The solution is periodic in time . As illustrated in Fig . 5-1 , the mass ...
Page 30
... motion is in its aid in understanding more complicated periodic motion . How can we improve our model to account for the experimental observa- tion that the amplitude of the mass decays ? Perhaps when the restoring force was ...
... motion is in its aid in understanding more complicated periodic motion . How can we improve our model to account for the experimental observa- tion that the amplitude of the mass decays ? Perhaps when the restoring force was ...
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