Here’s the solution:

```
# Exercise 4: Visualise Results & Save
# Make a list of 100 x-values to plot the fit
xfit = linspace(0, 0.8, 100)
yfit = slope*xfit + intercept
# Plot Fit results
plot(xfit,yfit, 'r-', label='Linear Fit')
errorbar(sqrt(length), time, fmt='o', label='Data', xerr=dl, yerr=dt)
# Label Axes
xlabel('$\sqrt{L}$ [m$^{1/2}$]')
ylabel('Period [s] ')
# Add Legend
legend(loc='best') # best location to avoid hiding data
# Save figure as png file with 300dpi
savefig('PendulumData.png', dpi=300, format='png', bbox_inches='tight')
```

## So what’s going on ?

By now you should be able to manipulate functions and variables to make sense of the first two lines. You can check the numpy documentation for more information on the `linspace`

function:

`linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None)`

Essentially, it will return an array (type given by `dtype`

; automatically determined if `=None`

) of `num`

evenly spaced numbers over an interval starting at `start`

and ending at `stop`

(the `stop`

number itself can be ommited if `endpoint=False`

). If `retstep=True`

it will also return the spacing between the numbers. In the first line of code, we’re therefore creating an array of 100 numbers between 0 and 0.8. Make sure you understand conceptually why “yfit” is also an array by construction.

The `plot`

function, that we loaded from `matplotlib.pyplot`

, is a bit more flexible in terms of its arguments, as its role is mainly graphic : simply plotting the “xfit” and “yfit” arrays we give it, with a bunch of options. See here for the full details. In this solution, we’re asking for a red line labeled “Linear Fit”.

Similarly, `errorbar`

can take quite a number of options, detailed here. For the purpose of this exercise, we want to plot $\sqrt{L}$ on the x-axis and $T$ on the y-axis, with appropriate errors (defined earlier), and data points shown as circles (`fmt='o'`

). It turns out that the errors are too small compared to the scale of the graph to show properly; to check that they are really there and the code works, you can play around with the values of `xerr`

and `yerr`

.

Full marks are given only for a properly labeled and captioned plot, so don’t forget to set a legend and label your axes, including units (you can use $\LaTeX$ with `$...$`

). Save the output with `savefig`

(see the documentation here) and move on to the next exercise.