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The differential equation with its initial conditions that modeled the mechanical vibrations of a spring is given by mu" (t) + ku(t) = 0, u(0) = I, u' (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

The differential equation with its initial conditions that modeled the mechanical vibrations of a spring is given by mu" (t) + ku(t) = 0, u(0) = I, u' (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

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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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
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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