Real Eigenvalues: Example1
Example: Consider the harmonic oscillator with spring constant , damping constant , 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?
[First Order D.E.]
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