Consider two identical oscillators, each with spring constant k and mass m, in simple harm...
Consider two identical oscillators, each with spring constant k and mass m, in simple harmonic motion. One oscillator is started with initial conditions x0 and v0; the other starts with slightly different conditions, x0 + δx and v0 + δv.
a) Find the difference in the oscillators positions, x1(t) − x2(t), for all t.
b) This difference is bounded; that is, there exists a constant C, independent of time, for which 
holds for all t. Find an expression for C. What is the best bound, that is, the smallest value of C that works? (Note: An important characteristic of chaotic systems is exponential sensitivity to initial conditions; the difference in position of two such systems with slightly different initial conditions grows exponentially with time. You have just shown that an oscillator in simple harmonic motion is not a chaotic system.)
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