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 |
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