Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 56
... stability is not a difficult one . Basically , an equilibrium solu- tion of a time - dependent equation is said to be stable if the ( usually time- dependent ) solution stays “ near " the equilibrium solution for all initial conditions ...
... stability is not a difficult one . Basically , an equilibrium solu- tion of a time - dependent equation is said to be stable if the ( usually time- dependent ) solution stays “ near " the equilibrium solution for all initial conditions ...
Page 102
... stable if , for all initial conditions near x = x , and v = 0 , the displacement from equilibrium does not grow ... stable ( i.e. , c > 0 and k > 0 ) . Stable if c > 0 . Unstable if c < 0 . Unstable if c < 0 . Stable if c 0 ( sometimes ...
... stable if , for all initial conditions near x = x , and v = 0 , the displacement from equilibrium does not grow ... stable ( i.e. , c > 0 and k > 0 ) . Stable if c > 0 . Unstable if c < 0 . Unstable if c < 0 . Stable if c 0 ( sometimes ...
Page 201
... STABLE р 0 NEUTRALLY STABLE These results are summarized in Fig . 46-1 . A similar diagram appeared in Sec . 27 referring to the stability of an equilibrium position of a spring - mass system with friction . In this manner we are able ...
... STABLE р 0 NEUTRALLY STABLE These results are summarized in Fig . 46-1 . A similar diagram appeared in Sec . 27 referring to the stability of an equilibrium position of a spring - mass system with friction . In this manner we are able ...
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