P16_011.PDF

11. (a) Since the problem gives the frequency f =3 . 00 Hz, we have ω =2 πf =6 π rad/s (understood to

be valid to three signiﬁcant ﬁgures). Each spring is considered to support one fourth of the mass

m car so that Eq. 16-12 leads to

ω = k

4 m car

k = 1

4 (1450kg) (6 π rad / s) 2 =1 . 29

10 5 N / m .

(b) If the newmass being supported by the four springs is m total = 1450 + 5(73) = 1815 kg, then

Eq. 16-12 leads to

ω new = k

⇒

f new = 1

2 π

10 5

1815 / 4

=2 . 68 Hz .

4 m total

⇒

1 . 29