Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 63
... energy ; it is that portion of energy due to the motion of the x mass ( hence the term kinetic ) . [ * f ( x ) dx is the work * necessary to raise the 1 X1 mass from x1 to x . The force necessary to raise the mass is minus the external ...
... energy ; it is that portion of energy due to the motion of the x mass ( hence the term kinetic ) . [ * f ( x ) dx is the work * necessary to raise the 1 X1 mass from x1 to x . The force necessary to raise the mass is minus the external ...
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 77
... energy " * E consists only of kinetic energy . Again as a check , differentiate equation 22.2 with respect to t yielding equation 22.1 . The energy E is constant and determined from the initial conditions , E = 2 ; +8 ( 1 : where no ...
... energy " * E consists only of kinetic energy . Again as a check , differentiate equation 22.2 with respect to t yielding equation 22.1 . The energy E is constant and determined from the initial conditions , E = 2 ; +8 ( 1 : where no ...
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