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To get acquainted with the basics of plotting with `matplotlib`, let's try plotting how much distance an object under free-fall travels with respect to time and also, it's velocity at each time step.

If, you have ever studied physics, you can tell that is a classic case of Newton's equations of motion, where...

We know that under free-fall, all objects move with the constant acceleration of 9.8 m/s².

The above code gives us two `numpy` arrays populated with the distance and velocity data points.

Let's try to see, what kind of plot we get when we plot both distance and velocity in the same plot.

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<b>Fig. 1.3</b> Distance and Velocity are plotted against the same geometrical axis.

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Here, we run into some obvious and serious issues. We can see that since both the quantities share the same axis, but have very different magnitudes, the graph looks disproportionate. What we need to do is separate the two quantities on two different axes. This is where the second approach to making plot comes into play.

When using the OO interface, it helps to know how the `matplotlib` structures it's plots. The final plot that we see as the output is a 'Figure' object. The `Figure` object is the top level container for all the other elements that make up the graphic image. These "other" elements are called `Artists`. The `Figure` object can be thought of as a canvas, upon which different artists act to create the final graphic image. This `Figure` can contain any number of various artists.

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Courtesy of <a href="https://matplotlib.org/3.2.1/gallery/showcase/anatomy.html">matplotlib</a>.

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1. All of the items labelled in "blue" are `Artists`. `Artists` are basically all the elements that are rendered onto the figure. This can include text, patches (like arrows and shapes), etc. Thus, all the following `Figure`, `Axes` and `Axis` objects are also Artists.

Now, that we understand how plots are generated, we can easily solve the problem we faced, earlier. To make Velocity and Distance plot to make more sense, we need to plot each data item against a seperate axis, with a different scale. Thus, we will need one parent `Figure` object and two `Axes` objects.

This plot as it is, is still not very intutitive. We should add a grid and a legend. Perhaps, we can also change the color of the axis labels and tick labels to the color of the lines.

But, something very weird happens when we try to turn on the grid, which you can see [here](https://github.com/whereistejas/whereistejas.github.io/blob/master/assets/jupyter-nb/double-pendulum-part-1-basics-of-plotting.ipynb) at In Cell 8. The grid lines don't align with the tick labels on the both the Y-axes. We can see that tick values `matplotlib` is calculating on its own are not suitable to our needs, and thus, we will have to calculate them, ourselves.

2. The method `ax1.get_ybound()` returns a list which contains the maximum and minimum limits for that particular axis (which in our case is the Y-axis).

The same process is repeated for second axis.

In this part, we covered some basics of `matplotlib` plotting, covering the basic two approaches of how to make plots. In the next part, we will cover how to make simple animations. If you like the content of this blog post, if you have any suggestions or comments, drop me an email or tweet at me or ping me on IRC. Nowadays, you will find me hanging arounfd #matplotlib on Freenode. Thanks!

1. Each part, will have a list of references at the end of the post, mostly leading to appropriate pages of the documentation and helpful blogs written by other people. **THIS IS THE MOST IMPORTANT PART**. The sooner you get used to reading the documentation, the better.