What determines the natural frequency of a body?a)Position of the body with respect to force appliedb)Mass and speed of the bodyc)Oscillations in the bodyd)Elastic properties and dimensions of the bodyCorrect answer is option 'D'. Can you explain this answer?

Question

Accepted Answer

Natural frequency is the frequency at which a body tends to oscillate in the absence of any driving or damping force.
Free vibrations of any elastic body are called natural vibration and happen at a frequency called natural frequency. Natural vibrations are different from forced vibration which happen at frequency of applied force .

Answer

In Human body continue catabolic and anabolic process take place hence it is elastic whereas these process gave a shape of body which called dimensions

Answer

The natural frequency of a body is determined by its elastic properties and dimensions. This means that the way a body oscillates or vibrates depends on its inherent characteristics, such as its stiffness and size.

Elastic Properties:
The elastic properties of a body refer to its ability to deform under the application of a force and then return to its original shape once the force is removed. These properties are typically described by parameters like the Young's modulus, shear modulus, and bulk modulus. The higher the stiffness or rigidity of a body, the higher its natural frequency will be.

Dimensions:
The dimensions of a body also play a crucial role in determining its natural frequency. The natural frequency is inversely proportional to the square root of the mass and directly proportional to the square root of the stiffness. This means that a body with a larger mass will have a lower natural frequency, while a body with a smaller mass will have a higher natural frequency. Similarly, a body with larger dimensions (such as length or size) will have a lower natural frequency, while a body with smaller dimensions will have a higher natural frequency.

Combining Elastic Properties and Dimensions:
The relationship between the elastic properties and dimensions of a body can be understood by considering a simple example of a spring-mass system. In this system, a mass is attached to a spring, and when the mass is displaced from its equilibrium position and released, it oscillates back and forth.

The natural frequency of this system depends on both the stiffness of the spring (elastic property) and the mass of the object (dimension). A stiffer spring will have a higher natural frequency, as it requires more force to compress or extend it. Similarly, a larger mass will have a lower natural frequency, as it requires more force to accelerate it.

In conclusion, the natural frequency of a body is determined by its elastic properties, which describe its ability to deform and return to its original shape, and its dimensions, which affect its mass and overall size. These factors interact to determine how a body oscillates or vibrates when subjected to a force.

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