A football bobble-head figure sits on your car dashboard. The 93-g head of the f

Question

A football bobble-head figure sits on your car dashboard. The 93-g head of the figure is attached to a spring with a spring constant of k = 19 N/m (figure below). You are driving along a straight road when you notice a series of hoses lying across the road, perpendicular to your motion, that cannot be avoided, and you drive over them. If the hoses are spaced exactly 3.6 m apart, what speed should you avoid so your bobble-head figure does not sustain damage from its head vibrating too hard at maximum amplitude?

Explanation / Answer

basically we want to avoid a speed that creates a resonance of vibration resulting in addition of amplitude of the head of the bobble-head.

93 gm head on spring with spring constant 19 N/m

amplitude = 0.093*10/19 = 4.8 cm approx

frequency = (19/0.093)^0.5 = 14.29

14.29/2*3.14 = 2.27 hz

1/2.27 = 0.439 seconds.

so the distance of 3.6 m should not be covered in 0.439 seconds, so speed that should be avoided is = 8.2 m/s

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