Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 5
... equal the rate of change of the momentum mo , where è is the velocity of the mass and x its position : dx v = dt If ... equals its mass times its acceleration , easily remembered as " F equals ma . " The resulting accelera- tion of a ...
... equal the rate of change of the momentum mo , where è is the velocity of the mass and x its position : dx v = dt If ... equals its mass times its acceleration , easily remembered as " F equals ma . " The resulting accelera- tion of a ...
Page 52
... equal radian , the error is reduced to at most about 4 percent , yet even radian is not a parti- cularly small angle ... equals 1000л , but cos ( 1000π ) is not a good approximation to cos ( 1000.5 ) , ( since cos ( 1000л ) = 1 and cos ...
... equal radian , the error is reduced to at most about 4 percent , yet even radian is not a parti- cularly small angle ... equals 1000л , but cos ( 1000π ) is not a good approximation to cos ( 1000.5 ) , ( since cos ( 1000л ) = 1 and cos ...
Page 307
... equal zero since keeping x fixed p , may vary . Likewise op1 / dx is not necessarily zero since p1 may change keeping t fixed . In Figs . 67-3 and 67-4 we have assumed c > 0 . What is the sign of c ? Recall C = dp = da ( po ) . ( 67.4 ) ...
... equal zero since keeping x fixed p , may vary . Likewise op1 / dx is not necessarily zero since p1 may change keeping t fixed . In Figs . 67-3 and 67-4 we have assumed c > 0 . What is the sign of c ? Recall C = dp = da ( po ) . ( 67.4 ) ...
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