The sprung parts of a passenger car weigh 11.12 kN (2500 lb) and the unsprung parts weigh 890 N (200 lb). The combined stiffness of the suspension springs is 45.53 kN/m (260 lb/in) and that of the tires is 525.35 kN/m (3000 lb/in). Determine the two natural frequencies of the bounce motions of the sprung and unsprung masses. Calculate the amplitudes of the sprung and unsprung parts if the car travels at a speed of 48 km/h (30 mph) over a road of a sinewave form with a wavelength of 9.15 m (30 ft) and an amplitude of 5 cm (2 in).