It is normal for any site with any sort of traffic to see the "Your site has been limited within the past 24 hours," message in the cPanel -> Resource Usage section and this article will explain why.
We run CloudLinux on our servers which allows us to limit each user account in order to ensure server stability and speed for everybody - yourself included.
The most important fact to keep in mind when thinking about these limits is that you can and likely will hit these limits on almost a daily basis. The best analgoy is to compare your CPU usage to the accelerator pedal in a vehicle. One may need to press the pedal all the way to the floor to get moving quickly just as your account may use 100% of its CPU to process a request as quickly as possible.
In short - it's absolutely normal for your account to have spikes of 100% CPU usage and for your account to be 'limited' due to this. The limitation notice simply exists as you were, in fact, limited to the CPU allocation you have on your account and does not automatically, in and of itself, indicate a problem.
Here is a graph that shows the limits being hit and, as a result, the message "Your site has been limited within the past 24 hours" will show but this graph is absolutely normal:
In this case the average is actually 0% but you can see there are a couple of spikes to 100% which is why it reports that the site was limited.
When it comes to determining whether or not you're using too much resources generally you will need to look first to see if you're experiencing any faults which is displayed in the bottom graph in the cPanel -> Resource Usage section. If you are seeing faults there's a good chance you either need to optimize your site or possibly upgrade to a plan that provides more CPU. Optimizing such as installing and properly configuring a quality caching plugin is generally the best way to resolve the issue.
We do offer a tool called PHP X-Ray that can help identify optimization issues within your website.
