ringed and beated are not correct past tenses of these verbs. Rang and beat are the simple past tense for these verbs.
You could say
The world rang in the new year.
USC beat Michigan in Rose Bowl
if you wanted to express these things in past rather than present tense.
However, both of these sentences sound like 'headlines' and so do not necessarily follow normal grammatical rules. It is normal to use present tense in headlines even when they are about past events. It is also normal to exclude determiners etc (world instead of 'the world').