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An automobile has mass 990 kg (including passengers). It is pushed down by 1.9 cm for every additional 100 kg of passengers. It is driven with constant velocity 18.6 km/h on a horizontal washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 4.8 cm and 19 cm, respectively. The distance between the front and rear tires is an integer multiple of the wavelength of the sine curve. Find the amplitude of oscillation of the automobile, assuming it moves vertically as an undamped driven harmonic oscillator. Neglect the mass of the wheels and springs, and assume the wheels remain in contact with the road at all times.

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