A bead with mass m slides along a thin wire whose shape is described by the function z f

Chapter 11, Problem 4

(choose chapter or problem)

The Sliding Bead

A bead with mass m slides along a thin wire whose shape is described by the function z=f(x). When \(f^{\prime}\left(x_{1}\right)=0\), \(f^{\prime \prime}\left(x_{1}\right)>0\), and the system is undamped, the critical point \(\mathbf{X}_{1}=\left(x_{1}, 0\right)\) is a center. Estimate the period of the bead when x(0) is near \(x_{1}\) and \(x^{\prime}(0)=0\).

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