Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 19
... problem we should compare as much as possible our intuition about what should happen with what the formula predicts . If the two agree , then we expect that our formula gives us the quantitative effects for the given problem - one of ...
... problem we should compare as much as possible our intuition about what should happen with what the formula predicts . If the two agree , then we expect that our formula gives us the quantitative effects for the given problem - one of ...
Page 20
... problem are necessary . Perhaps the intuition is incorrect , in which case the mathematical formulation and solution has aided in directly improving one's qualitative ... problem the 20 Mechanical Vibrations INITIAL VALUE PROBLEM.
... problem are necessary . Perhaps the intuition is incorrect , in which case the mathematical formulation and solution has aided in directly improving one's qualitative ... problem the 20 Mechanical Vibrations INITIAL VALUE PROBLEM.
Page 21
... problem the mass is initially at rest . Two initial conditions are necessary since the differential equation involves the second derivative in time . To solve this initial value problem , the arbitrary constants c1 and c2 are determined ...
... problem the mass is initially at rest . Two initial conditions are necessary since the differential equation involves the second derivative in time . To solve this initial value problem , the arbitrary constants c1 and c2 are determined ...
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude of oscillation analyze approximation Assume birth c₁ calculation characteristics Consider constant coefficient corresponding d2x dt2 damping de/dt decreases delay depend derived determine difference equation discussed dx dt dx/dt energy integral equilibrium population equilibrium solution equivalent example exercise exponential Figure formula function growth rate Hint increases initial conditions initial value problem isoclines linearized stability analysis logistic equation mass mathematical model maximum method of characteristics motion moving N₁ Newton's nonlinear pendulum number of cars obtained occur ordinary differential equations oscillation P₁ partial differential equation period phase plane Pmax population growth potential energy r₁ result sharks shock Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solution curves solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow trajectories Umax unstable equilibrium position variables vector x₁ yields zero