This is normal because browser doesn't allow scripts to work across different domains such as http://mysite.com and http://www.mysite.com, thus for security policy scripts are blocked.

Although this issue could be also related and solved using correct Joomla settings.

Normally Joomla uses dynamic base address for the site, having a look at the Joomla configuration.php you can check that the variable named '$live_site' has empty value as by default.

Notice that you should always use only 1 domain for your website to have good SEO, so it's recommended that you redirect from one domain to another using the htaccess.

When Joomla routing resolves dynamically the site base address this will affect also the scripts, for this reason if the '$live_site' variable is not forced to a specific domain also scripts will work in any case.