Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 61
Page 7
... force , one should study the motions of spring - mass systems under different circumstances . Let us suppose a series of experiments were run in an attempt to measure the spring force . At some position the mass could be placed and it ...
... force , one should study the motions of spring - mass systems under different circumstances . Let us suppose a series of experiments were run in an attempt to measure the spring force . At some position the mass could be placed and it ...
Page 24
... force on mass m , and if F2 is the force on mass m2 , then d2x1 m1 dt2 = F1 and m2 d2x2 dt2 = F2 . x2 To complete the derivation of the equations of motion , we must determine the two forces , F , and F2 . The only force on each mass is ...
... force on mass m , and if F2 is the force on mass m2 , then d2x1 m1 dt2 = F1 and m2 d2x2 dt2 = F2 . x2 To complete the derivation of the equations of motion , we must determine the two forces , F , and F2 . The only force on each mass is ...
Page 30
... forces . What causes the amplitude of the oscillation to diminish ? Let us conjecture that there is a resistive force , that is , a force preventing motion . When the spring is moving to the right , then there is a force exerted to the ...
... forces . What causes the amplitude of the oscillation to diminish ? Let us conjecture that there is a resistive force , that is , a force preventing motion . When the spring is moving to the right , then there is a force exerted to the ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
80 other sections not shown
Other editions - View all
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