Question

Ignoring the damping introduced by the shock absorbers, explain why the number of passengers in a car affects the vibration frequency of the car’s suspension system.

How do you do figure out the answer to this question using only these formulas?

Fs=-kx

f=1/T

E=1/2kA^2

v=+/-sqrt(k/m(A^2-x^2)).

Answer 1

The force acting can be written as, Fs​​ = -kx

Now suppose if car is moving with some acceleration x'' then the force F​​​​​​s can be written in the form of : F​​​​​​s = mx''

Using above equations we have,

mx'' = -kx

Or x" = -(k/m) x

As acceleration is directly proportional to negative of x. This is a type of SHM. hence

w​​​​​​2​​​​​ = k/m or. f = swrt√(k/m)* (1/2π)

In the car k will remain unchanged and

If the no of passengers in the car increases then total mass will increase and hence the corresponding vibration frequency will decrease.