The Chasam Sofer makes a very interesting comment about Shemini Atzeres. He says that this particular Yom Tov does not have any special symbol or Mitzvah act that enhances our observance of the Yom Tov. He notes that on Pesach we have Matzah. On Shavuos we have the Shtei HaLecham – the 2 breads brought with the sacrifices of the day. On Sukkos we have the four species (commonly called Luvav and Esrog). On Rosh HaShanna we have the Sofar. And on Yom Kippur we fast.
On Shemini Atzeres we have only the holiness of the day. This says the Chasam Sofer is all we need. V’Hayisah Ach Sameach – Shemini Atzeres is all about the Simcha of Yom Tov. This is the focus on Shemini Atzeres.
As we complete this holiday season - my wish to all of my readers and commenters a truly joyous Yom Tov. Chag Sameach