Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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The differential equation with its initial conditions that modeled the mechanical vibrations of a spring is given by тu" (t) + ku(t) — 0, и(0) — 1, и' (0) - V where u(t) is the displacement of the body at time t. To rescale the model equation, we set y = 4, T= Then the new model becomes. m/k d'y + 4n?y(7) = 0, y(0) = 1, y'(0) = Vm/k !! O d'y + y(7) = 0, y(0) = 1, y'(0) = Vm/k O d²y + y(7) = 0, y(0) = 1, y'(0) = VE/m d7 2 d?y + y(T) = 0, y(0) = T, y'(0) = V k/m %3D %3D %3D dr O d'y + y(T) = 0, y(0) = 1, y'(0) = Vm/k %3D %3D o d'y + y(7) = 0, y(0) = 1, y'(0) = Vm/k %3D + y(7) = 0, y(0) =ym/k, y'(0) = 1 %3D d'y + y(T) = 0, y(0) = 1, y'(0) = 2n %3D
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Transcribed Image Text:The differential equation with its initial conditions that modeled the mechanical vibrations of a spring is given by тu" (t) + ku(t) — 0, и(0) — 1, и' (0) - V where u(t) is the displacement of the body at time t. To rescale the model equation, we set y = 4, T= Then the new model becomes. m/k d'y + 4n?y(7) = 0, y(0) = 1, y'(0) = Vm/k !! O d'y + y(7) = 0, y(0) = 1, y'(0) = Vm/k O d²y + y(7) = 0, y(0) = 1, y'(0) = VE/m d7 2 d?y + y(T) = 0, y(0) = T, y'(0) = V k/m %3D %3D %3D dr O d'y + y(T) = 0, y(0) = 1, y'(0) = Vm/k %3D %3D o d'y + y(7) = 0, y(0) = 1, y'(0) = Vm/k %3D + y(7) = 0, y(0) =ym/k, y'(0) = 1 %3D d'y + y(T) = 0, y(0) = 1, y'(0) = 2n %3D
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Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
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