Yet there is a halachah that if someone passes away the day before Shavuot, those who must mourn them essentially do not sit shiva. What's so weird about this? Shiva is named for the fact that it is a seven-day mourning period. When Shabbath falls during the shiva, we don't observe most of the minhagim associated with shiva, because one can't mourn outwardly on Shabbath.
When this mourning period falls before Pesah or Sukkoth, it's understandable that there is no real period of mourning, we are commanded to be happy on the festivals, and these festivals each last seven days in length, which means that there is no time left in which to observe the mourning period.
But what about Shavuot? It's only one day long, so if someone passed away right before Shavuot, why wouldn't the mourners be required to sit for the five days after Shavuot?
In order to answer this I need to share something with you about the true nature of time and the world to come. The world to come is called a day that is entirely long. What does this mean? Chazal explain in the hidden Torah that in this world, each day vies for it's time in the spotlight and since the days themselves cannot get along and work together, each day shines for twenty-four hours and then ceases, making room for another day to take over. In the world to come, the days dwell together peacefully and so they all shine at once, indefinitely.
From this perhaps we can see how Shavuot is a taste of the world to come and at the same time explain our quandry regarding the halachot of mourners after Shavuot. I would like to say that Shavuot is actually a seven-day festival just like her sister festivals. The difference is that on Shavuot all the days dwell in peace with one another, and so down here in this world, Shavuot is represented as only a single day -- yet when it comes to the laws pertaining to mourning, since Shavuot is the holiday representing the resurrection of the dead, so we count all seven days of Shavuot and negate the mourning period -- just as the ultimate resurrection will render mourning a moot point.