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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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