Real Eigenvalues: Example1

Example: Consider the harmonic oscillator with spring constant tex2html_wrap_inline96 , damping constant tex2html_wrap_inline98, and the mass m=1.

(1)
Write down the second order equation governing this physical system. Use the letter y for the spring's displacement from its rest position.
(2)
Convert this equation into a linear system of first order differential equations.
(3)
Solve the system.
(4)
Find the particular solution which satisfies the initial conditions

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(5)
Discuss the long-term behavior of the system. Is this conclusion probable?

Solution:

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[Differential Equations] [First Order D.E.]
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Author: Mohamed Amine Khamsi

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