Question

automobile can be considered to be mounted on four spring as for as vertical oscillations are cocerned the spring of a certain car of mass 1460 kg are adjusted so that the vibrations have a frequency of 2.95 HZ (a) find the force constant of each of the four spring assumed identically (b) what will be the vibration frequency 5% average in 70.3 Kg each ride in the car?​

Answer 1

Answer:

Answer

(a) Since the problem gives the frequency f=3.00Hz, we have ω=2πf=6πrad/s. Each spring is considered to support one fourth of the mass m

car

so that ω=

m

car

/4

k

⇒k=

4

1

(1450kg)(6πrad/s)

2

=1.29×10

5

N/m.

(b) If the new mass being supported by the four springs is m

total

=[1450+5(73)]kg=1815kg, then ω

max

=

m

total

/4

k

⇒f

new

=

2π

1

(1815/4)kg

1.29×10

5

N/m

=2.68Hz