We are given the equation:

$y = 2 \cos \left( x + \frac{\pi}{10} \right)$

To solve for the various properties:

1. Amplitude:

The amplitude is the coefficient in front of the cosine function. Here, it is $2$. Therefore, the amplitude is: $\boxed{2}$

Would you like to go over the details of how to find the period, phase shift, or vertical translation?

Here are some follow-up questions you might consider:

1. How is the period of a cosine function calculated?
2. What is the phase shift in this equation?
3. Is there any vertical translation in this function?
4. How does the coefficient of $x$ affect the frequency of the cosine wave?
5. How would the graph look if we replaced $\cos$ with $\sin$?

Tip: The phase shift in a cosine function is determined by the horizontal shift $(x + \frac{\pi}{10})$, and you should solve for it step by step.