Attitude Of Gratitude
One makes a berachah of Shehecheyanu on a mitzvah that comes at a specific time of the year. We recite the berachah of Shehecheyanu on every yom tov. Even Shemini Atzeres merits a Shehecheyanu because it is considered a new yom tov. We do not recite a Shehecheyanu at Kiddush or candle lighting on the last days of Pesach because those days are a conclusion of a yom tov on which we already recited Shehecheyanu on the first days. On the first day of Sukkos, one recites a Shehecheyanu when one takes the lulav for the first time that year. Similarly, a Shehecheyanu is recited on the mitzvah of shofar, megillah, and Chanukah lights. These mitzvos are not applicable year-round, and when we merit to fulfill them we thank Hashem for sustaining us so that we lived to ha’zeman ha’zeh, this time. Thankfully, we lived to the new season and we are able to fulfill those mitzvos.
The Gemara in Menachos says that someone recites a Shehecheyanu when bringing a minchah offering. However, the Gemara does not explicitly say who is bringing or what minchah is being brought. One explanation in the printed version of Rashi is that a kohen is reciting a Shehecheyanu when he offers the minchas ha’omer that was brought once a year, on the second day of Pesach. That would fit perfectly with the other mitzvos cited above. The kohen is thanking Hashem for allowing him to live until the second day of Pesach and fulfill this once-a-year mitzvah.