Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 63
... energy that is stored in the system for " potential " usage , and hence is called the potential energy ( relative to the position x = x1 ) . Equation 19.2 is called the equation of conservation of energy or the energy equation . The total ...
... energy that is stored in the system for " potential " usage , and hence is called the potential energy ( relative to the position x = x1 ) . Equation 19.2 is called the equation of conservation of energy or the energy equation . The total ...
Page 64
... energy more immediately yields the result . The potential energy relative to the ground level ( a con- venient position since there is no equilibrium for this problem ) is y F ( ) = mg dỹ = mgy . Conservation of energy implies that the ...
... energy more immediately yields the result . The potential energy relative to the ground level ( a con- venient position since there is no equilibrium for this problem ) is y F ( ) = mg dỹ = mgy . Conservation of energy implies that the ...
Page 66
... potential energy as F ( 0 ) = √ g sin Ō dē . 0 Evaluate this potential and formulate conservation of energy . ( d ) Show that this potential energy ( as a function of Ø ) has a relative mini- mum at the stable equilibrium position and ...
... potential energy as F ( 0 ) = √ g sin Ō dē . 0 Evaluate this potential and formulate conservation of energy . ( d ) Show that this potential energy ( as a function of Ø ) has a relative mini- mum at the stable equilibrium position and ...
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 |
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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