Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 74
... linear systems . Can you give a simple mathematical explanation of why for linear problems the period cannot depend on the amplitude ? [ Answer : For a linear ( homogeneous ) differential equation , if x ( t ) is a solution , then Ax ...
... linear systems . Can you give a simple mathematical explanation of why for linear problems the period cannot depend on the amplitude ? [ Answer : For a linear ( homogeneous ) differential equation , if x ( t ) is a solution , then Ax ...
Page 303
... linear partial differential equation while the exact traffic equation 66.1 is a nonlinear partial differential equation . The coefficient that appears in ... Linear Partial Differential Equation A LINEAR PARTIAL DIFFERENTIAL EQUATION.
... linear partial differential equation while the exact traffic equation 66.1 is a nonlinear partial differential equation . The coefficient that appears in ... Linear Partial Differential Equation A LINEAR PARTIAL DIFFERENTIAL EQUATION.
Page 399
... Linear algebra , 140-141 Linear damping force , 30 Linear oscillator , phase plane , 70-75 Linear partial differential equations , 303- 308 Linearization , 156-158 , 168-169 , 189 , 301-303 , 370-371 Linearized pendulum ( see also ...
... Linear algebra , 140-141 Linear damping force , 30 Linear oscillator , phase plane , 70-75 Linear partial differential equations , 303- 308 Linearization , 156-158 , 168-169 , 189 , 301-303 , 370-371 Linearized pendulum ( see also ...
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