Chapter 3, Problem 3.18P

What is Logarithmic Decrement in damped vibration? A heavy machine, weighing 3000 N, is supported on a resilient foundation. The static deflection of the foundation due to the weight of the machine is found to be 7.5 cm. It is observed that the machine vibrates with an amplitude of 1 cm when the base of the foundation is subjected to harmonic oscillation at the undamped natural frequency of the system with an amplitude of 0.25 cm. Find a. the damping constant of the foundation, b. the dynamic force amplitude on the base, and c. the amplitude of the displacement of the machine relative to the base.

The figure below shows a simple model of a motor vehicle that can vibrate in the vertical direction while traveling over a rough road. The vehicle has a mass of 1200 kg. The suspension system has a spring constant of 400 kN/m and a damping ratio of ζ = 0.5. If the vehicle speed is 20 km/hr, determine the displacement amplitude of the vehicle. The road surface varies sinusoidally with an amplitude of  Y=0.05m and a wavelength of 6 m.   (please use the second images' conditions to answer the question above) (Also, please submit screenshot of matlab)

The amplitude of the steady-state response of a single-degree-of-freedom device is x=5 mm, when the excitation frequency is Ω=ωn. System mass m=200 kg. Fastening stiffness k=30 kNm and damping ratio ς=0.1. The system is loaded by the force F(t)=e^(i*Ω*t). How much must the excitation frequency be changed in order for the amplitude of the device to decrease to the value x=1 mm?

2.  A mass m = 2.5 kg is suspended by a spring of stiffness constant s = 40 Nm-1. The amplitude of the vertical oscillations of the system is observed to decrease to 20 % of the initial value after five consecutive cycles of oscillations. Determine the damping coefficient Rm of the system. Select one: a. 0.75 b. 1 c. 1.25 d. 0.5 e. 0.25

A mass of 12 ks is attached to two springs each of stiffness 4000 N/m and mounted in parallel. What is the natural frequency of the system? Answer: 25.8 rad/s

The amplitude of vibration of an undamped system is measured to be 1 mm. The phase shift from t = 0 is measured to be 2 rad and the frequency is found to be 5 rad/s. Determine the initial displacement. *         3.6 mm/s       - 2.1 mm/s       - 7.4 mm/s       6.1 mm/s

A mass of 36.3 kg is carried on an elastic system of stiffness 350 kN/m, and carries an absorber consisting of a mass 3.18 kg attached to it by a spring of stiffness 1 kN/m. Write down the equations of motion of the compound system and solve them to find the natural frequencies of the system and the corresponding amplitude ratios. [7.37 Hz; (X2/X1)= 39.8; 15.83 Hz; (X₂/X₁)= -0.2]