You can definitely constrain your Google search results by time, but it's one of the many types of searches that are best started by going to the Advanced Search Page rather than just searching from the home page or within your Browser navbar. On that page you'll see:

Lots of options, as you can see, but notice in particular "Return web pages first seen in the" and a pop-up menu of options. I've selected "last week" and that will constrain our search results to being just those pages that have been added to the index in the last 7 days.

Execute a search like this, though, and notice the additional parameter on the search URL. For example: "stompernet" appears in the text of the page and it's been added to Google in the last week. Click on that and notice that the search results includes the nice little box:

Once you've done one date constraint, you can clearly chose other settings easily enough!

The URL's scary-long, but there's one parameter we want to see since it's fun and easy to play with this date constraint parameter:

Confusing, but other folk have done the decoding here (notably here and here) so we can learn that in this instance w stands for "week", and that "d" is day and "y" is years. As explained:

Armed with this knowledge, here's a really simple search for pages that have referenced "atlanta" in the last day:

Got it? Now, go wild hacking those Google URLs! :-)