A machine part of mass 1.95 Kg vibrates in a viscous medium. Determine the damping coefficient when a harmonic exciting force of 24.46 N results in resonant amplitude of 1.27 cm with a period of 0.20s.

You are to investigate the vibration properties of the shock absorber system of a 2000 kg car. The shock absorbers drop 10 cm when the car is lowered from the lift and stands on its wheels. In addition, the amplitude decreases by 50% with each oscillation. Assume that the weight of the car is distributed evenly over all wheels and use the above information to determine the values ​​for the spring constant k and the damping coefficient b. What error does the calculation deliver if the natural frequency of the shock absorbers ω is approximated by that of the undamped system ω_0?

A particular naturally vibrating system is subject to damping. The system consists of a small mass m = 0.1 kg, the system stiffness k = 200 Nm-1 and the damping coefficient c = 0.25 kgs-1 . Determine the values of the natural and damped frequencies, the damping factor, damping ratio, periodic time and logarithmic decrement. Sketch and describe the nature of the motion

Assume that you are examining the characteristics of a suspension system of a 2000 kg automobile. The suspension "sags" 10 cm when the weight of the entire automobile is placed on it. In addition, the amplitude of the oscillation decreases by 50% during one complete oscillation. Estimate the values of k and for the spring and shock absorber system of each wheel. Assume each wheel supports 500 kg.