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 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др