Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 77
... yields an expression for L / 2 ( d0 / dt ) 2 , the kinetic energy , which must be positive . Figure 22-2 gives a graphical representation of L / 2 ( d0 / dt ) 2 dependence on 0 , which is easily related to de / dt dependence on 0 . -π ...
... yields an expression for L / 2 ( d0 / dt ) 2 , the kinetic energy , which must be positive . Figure 22-2 gives a graphical representation of L / 2 ( d0 / dt ) 2 dependence on 0 , which is easily related to de / dt dependence on 0 . -π ...
Page 127
... yield is defined as the total interest at the end of the year divided by the money on deposit at the beginning of the year . ( a ) What is the yield ? ( b ) Evaluate the yield if n = 1 or n = 2 . 32.6 . The yield ( derived in exercise ...
... yield is defined as the total interest at the end of the year divided by the money on deposit at the beginning of the year . ( a ) What is the yield ? ( b ) Evaluate the yield if n = 1 or n = 2 . 32.6 . The yield ( derived in exercise ...
Page 159
... yields 1 1 / a = + N ( a - bN ) N a b / a bN ' | - In | N | --In | a − bN | = t + c , where the absolute values in the resulting logarithms can be very important ! The arbitrary constant c enables the initial value problem , N ( 0 ) ...
... yields 1 1 / a = + N ( a - bN ) N a b / a bN ' | - In | N | --In | a − bN | = t + c , where the absolute values in the resulting logarithms can be very important ! The arbitrary constant c enables the initial value problem , N ( 0 ) ...
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