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3) Condider the differential equation + +y = 0 . i) What is the characteristic polynomial for this ODE? ii) Find the roots of the characteristic polynomial. iii) Using these, write the general solution of the ODE. iv) If this equation were the equation of a harmonic oscillator, would it be for an undamped, damped, critical or overdamper harmonic oscillator? Explain why.

3) Condider the differential equation + +y = 0 . i) What is the characteristic polynomial for this ODE? ii) Find the roots of the characteristic polynomial. iii) Using these, write the general solution of the ODE. iv) If this equation were the equation of a harmonic oscillator, would it be for an undamped, damped, critical or overdamper harmonic oscillator? Explain why.

Advanced Engineering Mathematics
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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+ + y = 0 . What is the characteristic polynomial for this ODE? d²y dx2 3) Condider the differential equation i) ii) iii) Using these, write the general solution of the ODE. Find the roots of the characteristic polynomial. iv) If this equation were the equation of a harmonic oscillator, would it be for an undamped, damped, critically damped or overdamper harmonic oscillator? Explain why.
Transcribed Image Text:+ + y = 0 . What is the characteristic polynomial for this ODE? d²y dx2 3) Condider the differential equation i) ii) iii) Using these, write the general solution of the ODE. Find the roots of the characteristic polynomial. iv) If this equation were the equation of a harmonic oscillator, would it be for an undamped, damped, critically damped or overdamper harmonic oscillator? Explain why.
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