P16_006.PDF

6. (a) Hooke’s law readily yields k = (15kg)(9 . 8m / s 2 ) / (0 . 12m) = 1225N / m. Rounding to three signiﬁ-

cant ﬁgures, the spring constant is therefore 1 . 23 kN/m.

(b) We are told f =2 . 00Hz = 2 . 00cycles / sec. Since a cycle is equivalent to 2 π radians, we have

ω =2 π (2 . 00) = 4 π rad/s (understood to be valid to three signiﬁcant ﬁgures). Using Eq. 16-12, we

ﬁnd

m = 1225N / m

(4 π rad / s) 2 =7 . 76 kg .

Consequently, the weight of the package is mg =76N.

⇒

ω = k