A classical mechanics problem by Steven Chase

A \(1 kg\) bead slides down a friction-less wire in the shape of the following curve, where \(x\) is the horizontal direction and \(y\) is the vertical direction.

\[\large{y = e^{-x/10} cos(x)}\]

There is a uniform downward gravitational acceleration \(g = 10 m/s^2\).

The bead starts at rest at \((x,y) = (0m,1m)\).

What is the magnitude of the net force on the bead when it is at the peak (zero-slope) in the vicinity of \(x = 4 \pi\)? Give your answer to 3 decimal places.


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