Consider a weakly-damped, but undriven oscillator as described by Equation (5.28). The general motion is given by (5.38). (a) Use this to sketch the state-space orbit, showing the movement of (x, ) for 0 ≤ t ≤10 with the parameters δ=0,ω1=2π, and β =0.5. (b) This system has a unique stationary attractor. What is it? Explain it, both with reference to your sketch and in terms of energy conservation.
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