Question

When five people whose average mass is 80 kg sit down in a car, they find that the car drops 0.91 cm lower on its springs. Then they get out of the car and bounce it up and down. The acceleration of gravity is 9.8 m/s 2 . What is the frequency of the car’s vibration if its mass (empty) is 3000 kg

Answer 1

Answer:1.91 Hz

Explanation:

Given

mass of each person $m=80 kg$

car lowers by $x=0.91 cm$

mass of car $m_0=3000 kg$

Weight of 5 person Pushes car by 0.91 cm

therefore

$5mg=kx$

where $k =spring\ constant$

$5\times 80\times 9.8=k\times 0.91\times 10^{-2}$

$k=435.55 kN$

and angular frequency of car is given

$w_n=\sqrt{\frac{k}{m_0}}$

$w_n=\sqrt{\frac{435.55\times 10^3}{3000}}$

$w_n=12.04 rad/s$

$2\pi f=w_n$

$f=\frac{w_n}{2\pi }$

$f=\frac{12.04}{2\times 3.142}=1.91 Hz$