An automobile with a mass of 1000 kg, including passengers, settles 1.0 cm closer to the road for every additional 100kg of passengers. It is driven with a constant horizontal component of speed 20km/h over a washboard road with sinusoidal bumps. The amplitude and wavelength of the sine curve are 5.0 cm and 20 cm, respectively. The distance between the front and back wheels is 2.4m. 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 that the wheels are always in contact with the road.