**Example:** Consider the harmonic oscillator with spring constant , damping constant , 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
**(5)**- Discuss the long-term behavior of the system. Is this conclusion probable?

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