Excerpt from Introduction to Non-Linear Mechanics

The spring constant in this case does not remain constant but diminishes with increasing 9. In this manner we obtain a more nearly correct representation of the motion. By retaining a greater number of terms in the power expansion of sin 0 we obtain still greater accuracy but the problem becomes more com plicated. In practice even the first approximation [3] gives an error of less than 1 per cent for angles of the order of 30 degrees.

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