An automobile, weighing 1000 lb empty and 3000 lb fully loaded, vibrates in a vertical direction while traveling at 55 mph on a rough road having a sinusoidal waveform with an amplitude Y ft and a period 12 ft. Assuming that the automobile can be modeled as a single-degree-of-freedom system with stiffness 30,000 lb/ft and damping ratio
determine the amplitude of vibration of the automobile when it is (a) empty and (b) fully loaded.