Question

A car of mass 1200kg has a suspension system where it's frame is supported by 4 equal springs, each has k = 20,000N/m. If two passengers of combined mass 170kg what will be the frequency of vibration of the car when it rides over a pothole?

Answer 1

F = ma = -kx

so \[\frac{ d^2x }{ dt^2 } = -\frac{ k }{ m } x\]

has a solution x = Acos(wt)

so \[\frac{ dx }{ dt } = \omega A Sin (\omega t) \]

and \[\frac{ dx }{ dt } = -\omega^2 ACos(\omega t)\]

therefore \[\omega^2 = \frac{ k }{ m }\]

\[ \omega = \sqrt{\frac{ k }{ m }}\]


\[\omega = \sqrt{\frac{ 20 000}{ 1370 }} = 3.82 Hz\]

Answer 2

Is the answer you're looking for 0.61 Hz ?

There are a couple of typo errors in the first bit, but your calculation of omega is correct.

Remember that omega is the angular frequency, so if the question just wants the normal frequency of the vibration, you need to divide omega by 2 pi to find f.

Answer 3

oops yes omega is two pi frequency. thanks, returning to uni in 20 odd days after a year out, this kinda stuff is going to hit me hard

Answer 4

I wish you well : )