B757 FLT CREW EXPERIENCES ENGINE FAILURE AT FL360 100 NM PAST ETP AND DIVERTS TO ENROUTE ALTERNATE FOR UNEVENTFUL LANDING.

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INTERNAL ENG FAILURE. IN CRUISE AT FL360 APPROX 100 MI PAST THE ETP; THE CAPT AND I HEARD A LOUD BANG FOLLOWED BY A SUDDEN SHUDDER OF THE ACFT. WE NOTED THAT WE HAD AN AMBER INDICATION OF N2 VIBRATION ON THE L ENG. WE IMMEDIATELY TURNED ON THE SEATBELT SIGN AND PULLED THE QRH FOR HIGH ENG VIBRATION. WE ALSO NOTED THAT WE WERE LOSING AIRSPD AND WOULD BE UNABLE TO MAINTAIN ALT. WE MADE THE DECISION TO TURN L OFF THE TRACK AND DSND AND DIVERT TO OUR ALTERNATE. I COMMUNICATED OUR INTENTIONS WITH ATC WHILE THE CAPT COMMUNICATED OUR POS AND INTENTIONS ON 121.5 AND 123.45. LNDG LIGHTS WERE TURNED ON. THE CAPT ALSO SPOKE WITH THE FLT ATTENDANTS TO LET THEM KNOW WHAT WE WERE DOING AND TO STAND BY. OUT OF FL290 WE TURNED DIRECT TO ZZZ AND SET UP FOR A CRUISE SPD OF 290 KTS AS DIRECTED BY THE DIVERSION PROCS. WE LEVELED OFF AT FL200. WE AGREED THAT IT WAS APPROPRIATE TO LEAVE THE ENG RUNNING RATHER THAN TO SHUT IT DOWN IN REF TO THE HIGH VIBRATION CHKLIST. WE ALSO COMPLETED THE ENG VIBRATION CHKLIST AND AGREED THAT WE WOULD USE THE SINGLE ENG DSCNT AND LNDG CHKLIST EVEN THOUGH NOWHERE IT REFED US TO DO SO. THE CAPT THEN COMMUNICATED WITH THE FLT ATTENDANTS. WE SPOKE WITH THE FLT ATTENDANTS SEVERAL MORE TIMES DURING THE COURSE OF THE ALMOST 3 HRS AFTER THE INITIAL DSCNT. THEY APPEARED TO BE CALM AND I WENT BACK TO USE THE RESTROOM 1 HR BEFORE LNDG AND OBSERVED THE PAX AND THE FLT ATTENDANTS ALL APPEARED TO BE CALM. AS A PRECAUTION WE REQUESTED EMER EQUIP TO BE STANDING BY FROM ZZZ APCH. I SPOKE WITH THE 'A' FLT ATTENDANT APPROX 15 MINS FROM LNDG AND LET HIM KNOW THAT WE WERE ANTICIPATING A NORMAL LNDG; THE CAPT SPOKE WITH THE FLT ATTENDANTS 5 MINS BEFORE LNDG TO GIVE THEM FURTHER INSTRUCTIONS. THE LNDG WAS NORMAL. AFTER WE HAD STOPPED ON THE RWY; THE CAPT MADE A PA TO THE PAX AND SPOKE WITH THE FLT ATTENDANTS. WE HAD AN UNEVENTFUL TAXI TO GATE WHERE GND CREW WAS WAITING FOR US. WE WERE MARSHALLED IN AND PAX WERE DEPLANED. HIGH N2 VIBRATION ON L ENG.