How to find number of user connections to an Oracle database between a specific time period?
That is what we have auditing for. Enable auditing, for example:

alter system set audit_trail=db scope=spfile;


You need to restart the database for this setting to take effect.

Audit logins:

audit create session;


If you created your database with DBCA, both the above are automatically enabled in 11.2.

Then you can query and browse logins in DBA_AUDIT_SESSION.