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 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
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analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др