Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 19
... formula shows that the period increases . The system oscillates more slowly ( is this reasonable ? ) . In any problem we should compare as much as possible our intuition about what should happen with what the formula predicts . If the ...
... formula shows that the period increases . The system oscillates more slowly ( is this reasonable ? ) . In any problem we should compare as much as possible our intuition about what should happen with what the formula predicts . If the ...
Page 37
... formula log ( 1 - x ) −x . Using this formula , damping is negligible ( with a 95 percent criteria ) if c2 2 4mk 2π = .0025 4π2 .00006 . This calculation has been simplified using the rough numerical approxima- tion 2≈ 10 , since π2 ...
... formula log ( 1 - x ) −x . Using this formula , damping is negligible ( with a 95 percent criteria ) if c2 2 4mk 2π = .0025 4π2 .00006 . This calculation has been simplified using the rough numerical approxima- tion 2≈ 10 , since π2 ...
Page 351
... formula is not valid if f ( x , t ) has a jump discontinuity between the two limits of integration . That is why we divided the integral above into two parts . Applying this well - known formula twice , yields xs d Xs dt [ p ] dx ; + ...
... formula is not valid if f ( x , t ) has a jump discontinuity between the two limits of integration . That is why we divided the integral above into two parts . Applying this well - known formula twice , yields xs d Xs dt [ p ] dx ; + ...
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