Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 35
... exponential . Thus we first sketch the exponential Ae - ct / 2m and its negative —Ae ̄ct / 2m in dashed lines . Periodically at the “ x's ” the solution lies on the two exponential curves drawn in Fig . 12-2 ( exactly where depends on ...
... exponential . Thus we first sketch the exponential Ae - ct / 2m and its negative —Ae ̄ct / 2m in dashed lines . Periodically at the “ x's ” the solution lies on the two exponential curves drawn in Fig . 12-2 ( exactly where depends on ...
Page 131
... exponential ( Nm 33.3 . Consider a species of animal which only breeds during the spring . Suppose that all adults die before the next breeding season . However , assume that every female produces ... Exponential Growth EXPONENTIAL GROWTH.
... exponential ( Nm 33.3 . Consider a species of animal which only breeds during the spring . Suppose that all adults die before the next breeding season . However , assume that every female produces ... Exponential Growth EXPONENTIAL GROWTH.
Page 132
... exponential behavior N ( t ) = NoeRotto ) , ( 34.3 ) as sketched in Fig . 34-1 for Ro > 0. A population grows exponentially if the growth rate is a positive constant . Similarly , a population decays exponentially if its growth rate is ...
... exponential behavior N ( t ) = NoeRotto ) , ( 34.3 ) as sketched in Fig . 34-1 for Ro > 0. A population grows exponentially if the growth rate is a positive constant . Similarly , a population decays exponentially if its growth rate is ...
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 |
Common terms and phrases
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