7 people whose average mass is 86 kg sit down in a car?

Question

& the car drops 0.98 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if its mass (empty) is 3743 kg (in units of Hz)? Acceleration of gravity is 9.8 m/s^2.

Answer 1

When the seven people get into the car it lowers to a new equilibrium position where the restoring force of the springs balances against the weight. Let m be the average mass of each individual then

k*x = 7*m*g

where k is the spring constant, x is the displacement caused by the seven people in the car, and g is the acceleration due to gravity.

Now you can solve for the spring constant associated with the car

k = 7*m*g/x

The bouncing car exhibits harmonic motion and is characterized by an angular frequency

w = sqrt(k/M)

where M is the mass on the unloaded car. Plugging in the known value for the spring constant

w = sqrt(7*m*g/(M*x))

The linear frequency is

f = w/(2*pi)

which will be in Hertz.