Dievsky V.A. - Solving problem D7 option 8 task 1

D7-08 (Task 1) Dievsky

For a given mechanical system shown in the diagram, it is necessary to determine the natural frequency of vibration.

A mechanical system in an equilibrium position can freely oscillate around the horizontal axis z passing through a fixed point O. The system consists of thin homogeneous rods 1 and 2 or a homogeneous plate 3, rigidly fastened to each other, as well as a point load 4. Mass of one meter of length rods 1 and 2 is 25 kg, the mass of plate 3 per square meter of area is 50 kg, and the mass of point load 4 is 20 kg. The stiffness coefficient of the elastic elements is c = 10 kN/m. The dimensions of the system parts are indicated in meters.

To determine the natural frequency of vibration of a given mechanical system, it is necessary to use the formula:

f = (1/2π) * √(k/m)

where k is the stiffness coefficient, m is the mass of the system.

Applying this formula, we get:

• for rods 1 and 2: f = (1/2π) * √(c/μ) = (1/2π) * √(10000/25) ≈ 5.03 Hz;
• for plate 3: f = (1/2π) * √(c/μ) = (1/2π) * √(10000/50) ≈ 3.55 Hz;
• for point load 4: f = (1/2π) * √(c/m) = (1/2π) * √(10000/20) ≈ 7.07 Hz.

Thus, the natural frequency of vibration of a given mechanical system depends on its configuration and can be determined by the formula.

Dievsky V.A. - Solving problem D7 option 8 task 1

that digital product is a solution to problem D7 option 8 task 1, which was developed by V.A. Dievsky. The solution is presented in the form of an electronic document and can be used for training, preparation for exams, as well as for independent work.

The document is designed in accordance with HTML standards, which makes it attractive and easy to read. The document contains a detailed description of the mechanical system shown in the diagram, as well as a formula for determining the natural frequency of vibration of this system.

This product is a useful resource for students and teachers of mechanics and physics, as well as for anyone interested in this field of science. Having received the solution to problem D7 option 8 task 1 from V.A. Dievsky, you will receive not only useful information, but also unique material developed by an experienced specialist in the field of mechanics.

Dievsky V.A. - The solution to problem D7 option 8 task 1 is a digital product, which is a solution to problem D7 option 8 task 1, associated with determining the natural frequency of vibration of a mechanical system. The solution to the problem was developed by V.A. Dievsky and presented in the form of an electronic document designed in accordance with HTML standards.

The document contains a detailed description of the mechanical system shown in the diagram and a formula for determining its natural frequency of vibration. To determine the natural frequency of vibration of a given mechanical system, the formula f = (1/2π) * √(k/m) is used, where k is the stiffness coefficient, m is the mass of the system. The document presents calculations of natural vibration frequencies for each part of the system: rods 1 and 2, plate 3 and point weight 4.

The solution to problem D7 option 8 task 1 can be used for training, preparation for exams, as well as for independent work. This product is a useful resource for students and teachers of mechanics and physics, as well as for anyone interested in this field of science. Having received the solution to the problem from V.A. Dievsky, you will receive not only useful information, but also unique material developed by an experienced specialist in the field of mechanics.

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Dievsky V.A. - Solution to problem D7 option 8 task 1 is a solution to a mechanical problem associated with determining the natural frequency of vibration of the mechanical system shown in the diagram. The system consists of bodies rigidly fastened to each other: thin homogeneous rods 1 and 2 or a homogeneous plate 3 and a point load 4, which can perform free oscillations around the horizontal axis z passing through a fixed point O.

To solve the problem, it is necessary to take into account the mass and dimensions of each part of the system: the mass of 1 m of the length of the rods is 25 kg, the mass of 1 m2 of the plate area is 50 kg, the mass of the point load is 20 kg, and the elastic elements have a stiffness coefficient c = 10 kN/m.

The solution to the problem is to determine the natural frequency of vibration of the mechanical system.

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