Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 92
Page 87
... Suppose that a spring - mass system satisfies m ( d2x / dt2 ) = −kx + αx3 , where a > 0. Sketch the solution in the phase plane . Interpret the solution ( see exercise 18.5 ) . 24.6 . Suppose that the potential energy is known ...
... Suppose that a spring - mass system satisfies m ( d2x / dt2 ) = −kx + αx3 , where a > 0. Sketch the solution in the phase plane . Interpret the solution ( see exercise 18.5 ) . 24.6 . Suppose that the potential energy is known ...
Page 264
... Suppose that the car labeled ẞ moves at the velocity 30 + 15ẞ ( dx / dt = 30 + 15ẞ ) and starts at t O at the position ẞL ( x ( 0 ) BL ) . ( a ) Show that the cars ' velocities steadily increase from 30 to 45 as ẞ ranges from 0 to 1 ...
... Suppose that the car labeled ẞ moves at the velocity 30 + 15ẞ ( dx / dt = 30 + 15ẞ ) and starts at t O at the position ẞL ( x ( 0 ) BL ) . ( a ) Show that the cars ' velocities steadily increase from 30 to 45 as ẞ ranges from 0 to 1 ...
Page 389
... Suppose that we approximate the rate of exiting cars as being proportional to the density , i.e. , B -yp . Assume that u = Umax ( 1 - P / Pmax ) . Under what conditions ( if any ) will a traffic shock occur ? [ Hint : See Sec . 80 ...
... Suppose that we approximate the rate of exiting cars as being proportional to the density , i.e. , B -yp . Assume that u = Umax ( 1 - P / Pmax ) . Under what conditions ( if any ) will a traffic shock occur ? [ Hint : See Sec . 80 ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
80 other sections not shown
Other editions - View all
Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
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