Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 6
... mass m1 and also a force F2 to m2 as seen in Fig . 2-3 : 1 Figure 2-3 . Newton's third law of motion , stating that the forces of action and reaction are ... mass could 6 Mechanical Vibrations NEWTON'S LAW AS APPLIED TO A SPRING-MASS SYSTEM.
... mass m1 and also a force F2 to m2 as seen in Fig . 2-3 : 1 Figure 2-3 . Newton's third law of motion , stating that the forces of action and reaction are ... mass could 6 Mechanical Vibrations NEWTON'S LAW AS APPLIED TO A SPRING-MASS SYSTEM.
Page 11
... mass is added , a result that should not be surprising . For a larger mass , the spring sags more . The stiffer the spring ( k larger ) , the smaller the sag of the spring ( also quite reasonable ) . It is frequently advantageous to ...
... mass is added , a result that should not be surprising . For a larger mass , the spring sags more . The stiffer the spring ( k larger ) , the smaller the sag of the spring ( also quite reasonable ) . It is frequently advantageous to ...
Page 23
... mass system initially at rest with initial displacement xo . Show that the maximum and minimum displacements occur halfway between times at which the mass passes its equilibrium position . 9. A Two - Mass Oscillator In the previous ...
... mass system initially at rest with initial displacement xo . Show that the maximum and minimum displacements occur halfway between times at which the mass passes its equilibrium position . 9. A Two - Mass Oscillator In the previous ...
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