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 |
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