B737-700 CREW WAS DISTRACTED BY ACFT VIBRATION; AND HAD AN ALT OVERSHOOT IN CZYZ CLASS E.

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ALTDEV. GOING THROUGH 10000 FT; STARTED ACCELERATING TO FMC RECOMMENDED CLB SPD OF 310 KTS. AS WE WENT THROUGH ABOUT 290-300 KTS I STARTED FEELING A VIBRATION BOTH IN CTL COLUMN AND RUDDERS. AT FIRST I THOUGHT IT MIGHT BE A GEAR DOOR; THEN I REALIZED IT MIGHT BE A LCO (LIMITED CYCLE OSCILLATION). I ASKED MY FO TO FEEL CTLS TO SEE IF HE FELT THE VIBRATION. HE FELT THE VIBRATION SO I BEGAN A MORE AGGRESSIVE CLB TO SLOW THE AIRSPD BACK TO BELOW 270 KTS. THE VIBRATION WENT AWAY AT ABOUT 280 KTS. WE WERE ASSIGNED 17000 FT. WE WENT THROUGH 16000 FT CLBING ABOUT 5000 FPM. I MUST HAVE HAD SOME PRESSURE ON THE CTL TRYING TO ANALYZE OUR VIBRATION PROB CONSEQUENTLY THE AUTOPLT DID NOT CAPTURE THE ASSIGNED ALT OF 17000 FT. I IMMEDIATELY DISCONNECTED THE AUTOPLT AND DSNDED BACK DOWN TO 17000 FT. WE HAD STOPPED AT 18000 FT. THERE WAS NO OTHER ACFT AROUND US AND TORONTO CLRED US UP TO 19000 FT BEFORE WE GOT BACK DOWN TO 17000 FT. I WAS DISTRACTED WITH THE VIBRATION PROB AND MISSED THE 'ONE-TO-GO' CALL MY FO MADE. WE DID NOT CLB THROUGH ANY ICING CONDITIONS. SUPPLEMENTAL INFO FROM ACN 560581: DURING CLB OUT OF 10000 FT; CAPT NOTICED VIBRATION IN CTLS AS WE ACCELERATED THROUGH 270 KIAS. WE WERE CLRED TO 15000 FT. WHILE IN THE CLB TO 15000 FT WE WERE ANALYZING THE VIBRATION AND SUBSEQUENTLY CLRED TO 17000 FT WHICH WE BOTH ACKNOWLEDGED. AT 16000 FT WE BOTH CALLED 'ONE TO GO' AND RETURNED OUR ATTN TO THE VIBRATION WHICH HAD NOW DISAPPEARED. AT THAT TIME I NOTICED WE HAD CLBED TO 17700 FT AND STILL CLBING; I CALLED 'ALT.' CAPT ACKNOWLEDGED AND CORRECTED BACK TO 17000 FT AFTER REACHING 18000 FT. CTR CTLR THEN CLEARED US TO FL190. AUTOPLT A WAS IN USE IN CMD MODE; BUT DID NOT CAPTURE THE ALT IN THE WINDOW. IT PROBABLY DID GO INTO ALT ACQUIRE BUT WAS FORCED OUT DUE TO THE AFT FORCE TO KEEP THE AIRSPD SLOW. BOTH OF US WERE SLOW TO NOTICE THIS DUE TO THE VIBRATION DISTR.