P16_008.PDF

8. (a) The acceleration amplitude is related to the maximum force by Newton’s second law: F max = ma m .

The textbook notes (in the discussion immediately after Eq. 16-7) that the acceleration amplitude

is a m = ω 2 x m ,where ω is the angular frequency ( ω =2 πf since there are 2 π radians in one cycle).

The frequency is the reciprocal of the period: f =1 /T =1 / 0 . 20 = 5 . 0 Hz, so the angular frequency

is ω =10 π (understood to be valid to two signiﬁcant ﬁgures). Therefore,

F max = mω 2 x m =(0 . 12kg)(10 π rad / s) 2 (0 . 085m) = 10 N .

(b) Using Eq. 16-12, we obtain

ω = k

⇒

k =(0 . 12kg)(10 π rad / s) 2 =1 . 2

10 2 N / m .