No Date

והניף את העמר לפני ה לרצנכם ממחרת השבת יניפנו הכהן.  The Sfas Emes (Pesach 5640) asks it should have said לרצנכם ממחרת השבת יניפנו הכהן for it is on that day we start counting, what is ממחרת?  He explains the Torah is saying from the day you start the waving process and it continues until Shavuot.  For although the physical act of waving the omer only takes place on the first day of chol hamoed Pesach the waving represents Klal Yisrael raising themselves to come close to Hashem.  The possuk says לרצנכם, why it is an obligation?  It hints to the idea that your desires should be channeled to be used to serve Hashem.  

Many commentators note that the Torah never gives a specific date for the holiday of Shavuot but instead the Torah just says 50 days after Pesach there is a holiday.  Why is this so?  On approach is that the holiday of Shavuot is the culmination of the holiday of Pesach.  On Pesach we became free but the freedom is only a means of becoming servants of Hashem as mentioned from Rav Yerucham.  The holiday of Shavuot as indicated in the name, weeks is a culmination of the preparation of the days and weeks of the omer bridging the gap between Pesach and Shavuot.  It is a process that starts ממחרת השבת and continues.  Rav Shmuel Rabinovitch suggests this a reason we read Rus on Shavuot.  The difference between Rus and Orpah is that Rus took the journey with Naomi all the way home but Orpah left; the lesson is that we must follow the path, the journey, all the way to the end.  

Another approach is that since Shavuot is the holiday celebrating the giving of the Torah, the Torah does not give a precise date for Torah can not be limited by time and space.  This approach is described in greater detail by Rav Steinsaltz.