Car Suspension Homework: Find Speed to Avoid Wild Bouncing

[nemixus]

Homework Statement

Assume your car’s suspension consists of 4 identical springs (one at each wheel). You notice that to support the mass of the car, each spring is compressed from its equilibrium length by 10 cm. The total “suspended” mass of your car is 1000 kg.
a) Determine the spring constant k of each of your suspension springs.
b) You drive with worn out shock absorbers over a roadway that has periodic small dips in it spaced 10 m apart (this can occur, for example, when the roadway is constructed by pouring concrete in uniform segments; the gaps between the smooth segments constitute such evenly spaced dips). What speed should you avoid, to prevent your car from bouncing wildly up and down?
(I already found a). Just need to do b), thanks)

Homework Equations

force downwards = mg = force radial = m*a (radial)

The Attempt at a Solution

So the car would not lift up when going over the bump so not to cause force upwards and making the car bounce
radius = r = 5 meters
force downwards = mg = force radial = m*a (radial)
mg = m*(v^2)/r
sqrt(g*r) = v
v = 7 m/s

 

[MalachiK]

I'm not sure where you got the radius in your attempt at solving this - but I think you're a little confused. Maybe you should think about how you could avoid resonance occurring - or for that matter, what are the conditions that would cause resonance to occur.