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1) Instead of eagerly anticipating the giving of the Torah, many people complacently went to sleep early!
2) At Har Sinai, says one Midrash, we wanted to accept only the written Torah. Hashem had to lift the mountain over our heads & threaten us before we would also accept the Oral Law. By concentrating on studying Talmud in our Shavuot learning we are showing our acceptance of Torah sheh B’al Peh.
The Zohar notes that Shavuot represents the wedding day of Am Yisrael the Kalla & HaKodesh Baruch Hu, the Chatan. Our hours of Torah study during Shavuot constitute the valuable "dowry" that we bring into the marriage!
