In Problems 17 through 20, analyze the critical points of the indicated system, use a computer system to construct an illustrative position–velocity phase plane portrait, and describe the oscillations that occur.

Example 2 in this section illustrates the case of damped vibrations of a soft mass-spring system. Investigate an example of damped vibrations of a hard mass-spring system by using the same parameters as in Example 2, except now with β = -5/4 < 0.

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Example 2 Damped soft spring Suppose that m = 1, c = 2, k = 5, and ß = . Then the nonlinear system in (13) is dx dt y, dy 3 · = −5x – 2y + 2x³ = −2y – 5x (1 – ½x²). dt (14)