An 1450 kg automobile has springs with k= 1.2×10*4 N/m.

Question

An 1450 kg automobile has springs with k= 1.2×10*4 N/m. One of the tires is not properly balanced; it has a little extra mass on one side compared to the other, causing the car to shake at certain speeds. If the tire radius is 41 cm, at what speed will the wheel shake most?

Answer 1

It would shake most at the natural frequency which occurs when the angular velocity (ω) is:

ω = √(k/m) where m = (vehicle mass)/4 = 362.5 kg

So ω = √(12000/362.5) = 5.754 radians/sec

Since the radius of the tire is 41 cm or 0.41 meters, the velocity is calculated from:

v = rω = 0.41(5.754) = 2.36 m/s