Now the OSX new system is free to upgrade, but my computer was brought in 2011.can i upgrade??

The short answer is "it depends". Have you consulted the "gurus" at the Apple Store? Or looked online on the Apple web site? Some things may be upgradeable (depending upon model you have), such as RAM or disc size. So, what are you trying to accomplish. Do bear in mind that Apple considers system of more than 2 or 3 years old to be "obsolete"...

Apple is normally really good at supporting older systems. I have a Mac that is 5 years old running Mavericks. Although I have upgraded the RAM. If you click the Apple icon on the top left and select 'About This Mac' what does it say.

How much Memory does it say you have and what is the processor. If you click More Info it will tell you the model and year your mac was made. The Mac I am typing this on is a Mac Book Air - Mid 2011 and it runs Mavericks really well.

All notebooks and iMacs built from 2011 and after are upgradable to Mavericks. You will also be able to install Yosemite when it is released. Please, next time give more details.

Before you attempt the upgrade, you may wish to ask yourself if it is really necessary. I find myself prefering Mountain Lion over Yosemite, and my computers are nice and stable. I find little motivation to upgrade if things are working exactly as I wish them to.