Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 76
... described by x ( t ) : = A sin ( @t + 0 ) , where @ = √k / m . Show that the total energy E satisfies = k E · A2 = 2 m2 v2 + mvz + 1⁄2 x 3 , k 2 2 where xo is the initial position and v 。 the initial velocity of the mass . 21.6 . The ...
... described by x ( t ) : = A sin ( @t + 0 ) , where @ = √k / m . Show that the total energy E satisfies = k E · A2 = 2 m2 v2 + mvz + 1⁄2 x 3 , k 2 2 where xo is the initial position and v 。 the initial velocity of the mass . 21.6 . The ...
Page 246
... described in an exercise in Sec . 50. Other predator - prey models are also discussed in the exercises in which the amplitudes of oscilla- tion decay as time goes on , as though nature seeks to restore predators and preys to an ...
... described in an exercise in Sec . 50. Other predator - prey models are also discussed in the exercises in which the amplitudes of oscilla- tion decay as time goes on , as though nature seeks to restore predators and preys to an ...
Page 254
... described by equation 54.6 . Can you predict the outcome of the competition . If c / d > a / b , which yeast has the highest tolerance of alcohol ? 54.7 . Consider equation 54.1 . ( a ) Give an ecological interpretation to the ...
... described by equation 54.6 . Can you predict the outcome of the competition . If c / d > a / b , which yeast has the highest tolerance of alcohol ? 54.7 . Consider equation 54.1 . ( a ) Give an ecological interpretation to the ...
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 |
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