A single degree of freedom system consists of a mass of 20 kg and a spring of stiffness 4000 N/m. The amplitudes of successive cycles are found to be 50, 45, 40, 35, ...mm. Determine the nature and magnitude of the damping force and the frequency of the damped vibration.

A spring extends by 5 centimeters when loaded vertically with 2.5kg of weight. A new weight of 1.75kg was attached to it and was displaced 6cm from its new equilibrium position and was released from rest. Determine the frequency of vibration in rad per second?

An automobile is modeled as a single-degree-of-freedom system vibrating in the vertical direction. It is driven along a road whose elevation varies sinusoidally. The distance from peak to valley () is 0.2 m and the distance along the road between the peaks is 35 m. If the natural frequency of the automobile is 2 Hz and the damping ratio of the shock absorbers is 0.15, determine the amplitude of vibration of the automobile at a speed of 60 km/hour. If the speed of the automobile is varied, find the most unfavorable speed for the passengers.

A weight attached to a spring of stiffness 3.0 lb/in has a viscous damping device. When the weight is displaced and released, the period of vibration is found to be 1.80 seconds and the ratio of consecutive amplitudes is 4.2 to 1.0. Determine the amplitude and phase angle when a force F-2cos(3t) acts on the system.