The structure shown in figure has a mass of 100 kg and a translational stiffness of 40,000 N/m. It is excited by a harmonic force having an amplitude Po = 500 N and an excitation frequency ω = 15 rad/s. The damping factor for the structure is ξ = 0.1. The initial conditions are u(0) = 6 cm and ώ(0) = 0. For the steady-state vibration determine: (a) The amplitude of the stady-state displacement. (b) Its phase with respect to the exciting force. (c) The maximum velocity and acceleration of the response. (d) Determine the equation that describes the total displaement of the structure as a function of time.

B/ Two massless springs with spring constants k1=100 and k2=150 are attached to mass of (m=20 kg) at A in parallel as shown in Fig (a). An identical pair of springs is attached to mass B in series as shown in Fig (b). Taking mA = mB = m, find and compare the natural frequencies ws and wp and (ws/wp) of the two systems. (b)

A machine of mass 112.7 kg is mounted on four parallel springs each of stiffness 3.2 x 105 N/m. When the machine operates at 58.0 Hz, the machine's steady state amplitude is measured as 0.5 mm. What is the magnitude of force transmitted to the foundations of the machine at this speed? The damping in the system is negligible. (Express answers to 3sf) Answer: 3.49

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A machine of mass 203.5 kg is mounted on four parallel springs each of stiffness 1.6 x 105 N/m. When the machine operates at 47.2 Hz, the machine's steady state amplitude is measured as 1.0 mm. What is the magnitude of force transmitted to the foundations of the machine at this speed? The damping in the system is negligible. (Express answers to 3sf) Answer:

A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator.  Find the damping ratio of the system  ζ . Find the transmissibility of the system,  Tf. Find the frequency ratio of the system, β.          Find the amplitude of the harmonic excitation force of the system,  Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X  in millimeters (mm).  Find the damped frequency of the system,  ωd  in rad/s. Find the force transmitted to the foundation,  FT  in Newton (N). Find the frequency of the harmonic…

answer question 2 and 3

The 1 degree of freedom underdamped vibration system is subjected to external force as shown in the figure. (1) Finding a steady state response. (2) Induce the frequency at which the maximum displacement occurs in detail and (3) Find the maximum displacement at that time. (4) Plotting the frequency response function and explain its concept.

Determine the equation of motion of the system in terms of the angle θ using the principle of virtual work. Assume the displacements are small. Determine the characteristic frequency of the structure?Determine the relative damping factor for the structure?

Consider the system in Figure 1-a, which is initially at equilibrium. The massless bar AOB with point mass m = 2 kg attached to B rotates with rotational viscous damping coefficient b about the fixed point system is connected by a horizontal spring (acting at B) to a fixed wall. The rotating bar has a length 3L=1.5 meters. L 2L k twine ww Figure 1-a A Rotational viscous damping coefficient b B g Massless a) Write the linearized equation of motion of the system (Figure 1-a) for small angular displacement 0 (t). (Symbolic)