What was found
RECEIVED A "SPS ADVANCED" ON EICAS AT 370, AT SAME TIME RECEIVED A BLINKING YELLOW IAS ON THE AIRSPEED INDICATOR ON BOTH PFD'S. STARTED DOWN TO 240 AND CAPTAIN`S AIRSPEED INDICATOR BLED OFF BELOW 200 KTS MEANWHILE STANDBY AIRSPEED AND F/O AIRSPEED SHOW 300 KTS AND WE WERE ALSO GETTING AN OVERSPEED AURAL WARNING OF "HIGH SPEED". THE CREW PRESSED THE ADC BUTTON ON THE CAPTS REVERSIONARY PANEL AND EVERYTHING APPEARED NORMALLY AGAIN BECAUSE CAPTAIN'S SIDE WAS BORROWING INFO FROM F/O'S SIDE. NOTE, THE CREW WERE IN NIGHT IMC CONDITIONS THE ENTIRE TIME. WITH AUTOPILOT ENGAGED THEY HAD AN UNCOMMANDED LEFT BANK. THE F/O DISCONNECTED THE AUTOPILOT AND FELT VIBRATION IN THE YOKE. IT GOT WORSE WHEN THEY WOULD TURN. IT WAS AN ALARMING HUMMING VIBRATING NOISE. THE CREW SLOWED BELOW 250 KTS AND IT DID GET A LITTLE BETTER BUT CONTINUED UNTIL LANDING. NOTICED A LOT OF CONDENSATION IN THE COCKPIT ON THE WINDOWS. UPON LANDING THE F/A REPORTED THE LIGHTS WERE FLICKERING IN THE CABIN AND CONDENSATION LEAKING ON A PASSENGER IN ROW 10A. PERFORMED MAX VMO EXCEEDANCE PHASE 1 INSP FOR AURAL WARNING "HIGH SPEED" WARNING. NO DEFECTS NOTED IAW AMM TASK 05-50-04-212-001-A00. REQUIRES DFDR DATA ANALYSIS TO DETERMINE PHASE 2 AND 3 DISPOSITION WITHIN 10 FC PER AMM 05-50-04 TABLE 604. COMPLIED WITH WORKCARD 12-200-01 THRU STEP 3 OF CLOSE JOB. FCF REQUIRED. NO DEFECTS NOTED AT THIS TIME. AEA WC 12-200-01 VIBRATION- DETAILED VISUAL INSPECTION STEPS 4 THRU 5 C/W. FCF WAS SATIFACTORY. THE AIRCRAFT WAS RETURNED TO SERVICE.