Real Eigenvalues: Example1

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

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


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


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

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