The undamped free vibration of system can be described by the following ODE: a?u(t) + 02и(t) — 0, и(0) — 1, й (0) — 0, tE (0,T] at? in which, w is the angular frequeney of vibration and I is the amplitude of vibration, both are constants. a) Use an appropriate second order accurate approximation to the 2nd order derivative in the above ODE to formulate the approximation solution to the ODE.
The undamped free vibration of system can be described by the following ODE: a?u(t) + 02и(t) — 0, и(0) — 1, й (0) — 0, tE (0,T] at? in which, w is the angular frequeney of vibration and I is the amplitude of vibration, both are constants. a) Use an appropriate second order accurate approximation to the 2nd order derivative in the above ODE to formulate the approximation solution to the ODE.
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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![The undamped free vibration of system can be described by the following ODE:
a?u(t)
+ w²u(t) = 0, u(0) = 1, ú(0) = 0, te (0,T]
at2
in which, w is the angular frequency of vibration and I is the amplitude of vibration, both are constants.
a) Use an appropriate second order accurate approximation to the 2nd order derivative in the above
ODE to formulate the approximation solution to the ODE.
b) Write the computation algorithm (step-by-step pseudo-code) for solving the ODE.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77d6a395-8141-49be-94ec-5a8172ba9d0f%2Fe28dc689-a537-4f7e-9586-716988626ba7%2Ffjje3xd_processed.png&w=3840&q=75)
Transcribed Image Text:The undamped free vibration of system can be described by the following ODE:
a?u(t)
+ w²u(t) = 0, u(0) = 1, ú(0) = 0, te (0,T]
at2
in which, w is the angular frequency of vibration and I is the amplitude of vibration, both are constants.
a) Use an appropriate second order accurate approximation to the 2nd order derivative in the above
ODE to formulate the approximation solution to the ODE.
b) Write the computation algorithm (step-by-step pseudo-code) for solving the ODE.
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