Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 21
... satisfies the initial conditions . For example , at t = 0 , x = xo . Thus C1 = Χρ . In general the velocity is obtained by differentiating the formula for dis- placement : dx dt = -c1w sin wt + c2w cos wt . In this problem the mass is ...
... satisfies the initial conditions . For example , at t = 0 , x = xo . Thus C1 = Χρ . In general the velocity is obtained by differentiating the formula for dis- placement : dx dt = -c1w sin wt + c2w cos wt . In this problem the mass is ...
Page 66
... satisfies m ( d2x / dt2 ) = −kx . ( a ) Derive that ( dx \ 2 k m ( d ) 2 + x2 = constant = E. 2 dt 2 ( b ) Consider the initial value problem such that at t = 0 , x = xo and dx / dt = vo . Evaluate E. ( c ) Using the expression for ...
... satisfies m ( d2x / dt2 ) = −kx . ( a ) Derive that ( dx \ 2 k m ( d ) 2 + x2 = constant = E. 2 dt 2 ( b ) Consider the initial value problem such that at t = 0 , x = xo and dx / dt = vo . Evaluate E. ( c ) Using the expression for ...
Page 301
... satisfies p ( x , 0 ) = COS X. = p2 which satisfies p ( x , 0 ) = sin x . 65.2 . Determine the solution of dP / dt 65.3 . Determine the solution of dp / dt = p , which satisfies p ( x , t ) along x = -2t . = 65.4 . Is there a solution ...
... satisfies p ( x , 0 ) = COS X. = p2 which satisfies p ( x , 0 ) = sin x . 65.2 . Determine the solution of dP / dt 65.3 . Determine the solution of dp / dt = p , which satisfies p ( x , t ) along x = -2t . = 65.4 . Is there a solution ...
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