Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 41
... equilibrium position more than once . The mass crosses its equilibrium position only if the initial velocity is sufficiently negative ( assuming that the initial position is positive ) . - When c2 4mk , the spring - mass system is said ...
... equilibrium position more than once . The mass crosses its equilibrium position only if the initial velocity is sufficiently negative ( assuming that the initial position is positive ) . - When c2 4mk , the spring - mass system is said ...
Page 58
... equilibrium position ) . In this case we say the equilibrium position is stable . * This shows the importance of simple harmonic motion as it will describe motion near a stable equilibrium position . For slight departures from ...
... equilibrium position ) . In this case we say the equilibrium position is stable . * This shows the importance of simple harmonic motion as it will describe motion near a stable equilibrium position . For slight departures from ...
Page 109
... equilibrium position , in which case we would say the equilib- rium position is stable ; or ( b ) the trajectories could " circle " around the equilibrium position ( that is , the trajectories would be closed curves ) , in which case we ...
... equilibrium position , in which case we would say the equilib- rium position is stable ; or ( b ) the trajectories could " circle " around the equilibrium position ( that is , the trajectories would be closed curves ) , in which case we ...
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