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Question: How can I playback the videos on an HDTV?

I really like this camer specially the 60fps feature. But I tried some samples from a 1920 X 1080 / 60p at 24Mbps aon my 46' LCD and the picture is shaky, and there is a lag between the sound and the picture. My Media player cannot handle the 60p format, neither can my pc. Is there a way to be able to playback the videos on a big HDTV with a good outcome?