The main reason for the second day Yom Tov is because in the times of the Beis Hamikdash when we decided to declare months based on the seeing the new moon there where certain places that the messengers of Beis Din would not get to, Hence they held two days because of a Safek and today people who live outside of Eretz Yisroel continue to keep two days even when we are in Ertez Yisroel Because of Minhag Avosenu Byodanu.With that said Why on Shavous where we know that Shavous is 50 days after Pesach why have the second day,as even if the Messenger would not have come on time we would have known based on the counting of days from Pesach?
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As per this article (http://www.chabad.org/library/article_cdo/aid/93594/jewish/Shavuos.htm)
And as per this article as well (http://www.ottmall.com/mj_ht_arch/v23/mj_v23i68.html#CUJ)