CL65 CREW HEARD A LOUD BANG AFTER TKOF. THE EICAS VIBRATION MONITOR FOR #2 ENG SHOWED EXCESSIVE VIBRATION.

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ON MAR/THU/04 AT APPROX XA30 IN TORONTO; CANADA; WE DEPARTED RWY 23 ENRTE TO CINCINNATI ON AN RJ FLT. WE HAD 15 PAX AND 3 CREW MEMBERS. SHORTLY AFTER TKOF; THERE WAS A LOUD BANG HEARD FROM ONE OF OUR ENGS. WE QUICKLY DETERMINED THAT IT WAS THE R ENG AND OBSERVED A VIBRATION MESSAGE ON OUR EICAS N2 GAUGE. WE WERE BELOW 1000 FT MSL AND THE ACFT WAS SHAKING VIOLENTLY. THE N1 GAUGES ON BOTH ENGS SHOWED THAT THE APR HAD GIVEN US THE 2% THRUST. WE REMAINED IN CTL OF THE ACFT AND CONTINUED TO CLB. WE NOTIFIED THE TWR CTLR; WHO INSTRUCTED US TO FLY THE ASSIGNED SID AND NOTIFY DEP CTL OF OUR PROB. WE WERE A BIT LATE IN THE TURN ON THE SID BECAUSE WE WERE PREOCCUPIED WITH THE ENG PROB. WE NOTIFIED DEP OF OUR SIT AND DECLARED AN EMER. WE ASKED FOR VECTORS BACK TO THE ARPT FOR AN EMER LNDG AND ALSO REQUESTED THAT CFR BE CALLED OUT AS A PRECAUTION. WE RAN ALL CHKLISTS INCLUDING THE ABNORMAL N2 VIBRATION QRH PROC. WE INFORMED THE FLT ATTENDANT AND PAX OF THE SIT. WE ALSO NOTIFIED OUR TORONTO OPS THAT WE WERE RETURNING TO THE GATE. WE TOLD ATC WE WERE READY FOR THE APCH BACK TO RWY 23. AS WE WERE INTERCEPTING THE LOC TO RWY 23; WE THEN FELT THE YAWING MOTION AND THRUST DECREASE OF AN ENG FAILURE. WE INSTANTLY RECEIVED THE R ENG OIL PRESSURE WARNING MESSAGE. WE ASKED ATC FOR ANOTHER VECTOR AND LEVELOFF AS TO RUN ANOTHER REQUIRED CHKLIST. WE LEVELED OFF AT 3000 FT AND GOT A R TURNOUT. WE THEN STARTED TO PERFORM THE MEMORY ITEMS FOR 'SEVERE ENG DAMAGE INFLT' WHEN THE R ENG STARTED TO SHOW SIGNS THAT IT WAS RUNNING AGAIN. WE DID SOME CHKS AND DETERMINED THAT THE ENG WAS RESPONSIVE TO THRUST LEVER INPUT. ALTHOUGH WE WERE ONLY GETTING AROUND 25% THRUST OUT OF THE BAD ENG; WE DECIDED TO KEEP IT RUNNING. WE WERE VECTORED AND CLRED FOR THE ILS TO RWY 23. THE APCH AND LNDG WERE UNEVENTFUL. WE TAXIED TO THE GATE AND DEPLANED OUR PAX. MAINT MET THE ACFT AT THE GATE AND I PERSONALLY SPOKE WITH OUR FLT DISPATCHER BY TELEPHONE. THE IRREGULAR OPS RPT WAS FILLED OUT AND TURNED IN TO THE COMPANY UPON ARRIVING IN CINCINNATI ON MAR/THU/04.