How do these two solutions compare?

We already know the numerical approach means sacrificing getting to an exact formula, but that it does enable us to plot our motion equations. But are we also sacrificing accuracy as well? The answer is the results are nearly identical and for the cycling force equation, nearly identical using a time interval of 1 second.

Comparing Results

The following are the results using the two approaches.

As you can see that even using a relatively large time interval, both solutions yielded nearly identical graphs. The direct solution does justify its additional complexity by identifying the shape of the curve as Tanh reflecting an underlying Hyperbola.

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