Is there a non-iterative way to solve for the motion of an object under the influence of a time-dependent, position-dependent force?(adsbygoogle = window.adsbygoogle || []).push({});

Here is an example problem:

A bead on a straight wire is subjected to a net force.

There is no friction between the bead and the wire.

The bead and the wire do not experience any gravitational forces.

The bead has a mass of 1kg.

The net force acts along the wire, and is position and time dependent. It can be represented as

F = 9x^{2}+ 5xt - 10t^{2}

The bead starts at rest at x = 0.

Where is the bead after 30 seconds have elapsed?

How would one go about solving a problem like this numerically?

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# The motion of an object acted on by a time-dependent, position-dependent force?

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