Serway & Jewett — Oscillatory Motion: Problem 16

While driving behind a car traveling at \(3.00 \text{ m/s}\), you notice that one of the car's tires has a small hemispherical bump on its rim as shown in Figure P15.16. (a) Explain why the bump, from your viewpoint behind the car, executes simple harmonic motion. (b) If the radii of the car's tires are \(0.300 \text{ m}\), what is the bump's period of oscillation? (c) What If? You hang a spring with spring constant \(k = 100 \text{ N/m}\) from the rear view mirror of your car. What is the mass that needs to be hung from this spring to produce simple harmonic motion with the same period as the bump on the tire? (d) What would be the maximum speed of the hanging mass in your car if you initially pulled the mass down \(8.00 \text{ cm}\) beyond equilibrium before releasing it?