Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 15
... oscillation repeats itself every T units of time , called the period of oscillation . Mathematically a function f ( t ) is said to be periodic with period T if f ( t + T ) = f ( t ) . = To determine the period T , we recall that the ...
... oscillation repeats itself every T units of time , called the period of oscillation . Mathematically a function f ( t ) is said to be periodic with period T if f ( t + T ) = f ( t ) . = To determine the period T , we recall that the ...
Page 174
... oscillation initially ( i.e. , at m = 0 ) to be c + c , while yo = c , from equation 41.4 . ] If the amplitude of oscillation grows , let us compute the number of intervals m , it takes for the amplitude to double : Ir1ma = 2 . ma = In ...
... oscillation initially ( i.e. , at m = 0 ) to be c + c , while yo = c , from equation 41.4 . ] If the amplitude of oscillation grows , let us compute the number of intervals m , it takes for the amplitude to double : Ir1ma = 2 . ma = In ...
Page 184
... oscillation in parts ( a ) and ( b ) . ( d ) Compare doubling times of the amplitude of oscillation . Reconsider exercise 42.10 with a = 10 . 42.12 . How might equation 42.5 be modified to prevent negative populations ? 42.13 . The ...
... oscillation in parts ( a ) and ( b ) . ( d ) Compare doubling times of the amplitude of oscillation . Reconsider exercise 42.10 with a = 10 . 42.12 . How might equation 42.5 be modified to prevent negative populations ? 42.13 . 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