For the system shown in Figure 1, the natural frequency of the system is 170 Hz. The rod has length 15 m and cross section area 37 cm2. The stiffness of the springs (K) is 131 N/m and the mass attached to the massless rod is 6 kg. Determine the Young’s modulus of the rod in GPa.

Please solve this problem by showing the manual calculation and choose the correct answer(SUBJECT: mechanical vibrations)

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A 2.50-kg object is attached to a spring with a force constant of 4.50 N/m. The object rests on a horizontal surface that has a viscous, oily substance spread evenly on it. The object is pulled 15.0 cm to the right of the equilibrium position and set into harmonic motion. After ?1=2.00 s the amplitude has fallen to 7.00 cm due to frictional losses in the oil. Calculate the damping constant ? for the oil.

a string is attached to a mechanical vibrator, which has a frequency of 30Hx. the sttring is 3.0m long and has a linear density of .4 g/cm. the tension is varied by adding weights to teh string passing over the pully. What tension is needed to cause the string to resonate with the vibrator in four segments. assume that he points where the string meets the vibrator and the pulley are approx nodes.

A 1-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.3 m and reaches a maximum speed of 5 m/s. What is the spring constant in N/m?

A concrete part with a mass of 800 kg is hung on a 6 m long steel cable. You determine the spring constant to be 3.924 \times 10 ^ 6 N/m. What is the oscillation period when the steel beam oscillates in the direction of the cable? Provide the result in seconds.

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…

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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…