Solution to problem 13.6.2 from the collection of Kepe O.E.

13.6.2 It is necessary to determine the coefficient of dynamic compliance of a body that is suspended from a spring and subject to a vertical driving force F = 30 sin 20t, provided that the angular frequency of the body’s natural oscillations is k = 25 rad/s. The answer to the problem is 2.78.

To solve this problem, it is necessary to use the formula for calculating the coefficient of dynamic compliance Sd = F / (mg), where F is the force acting on the body, m is the mass of the body, g is the acceleration of gravity.

Considering that the angular frequency of the body’s natural oscillations is k = 25 rad/s, the period of oscillations is T = 2π / k ≈ 0.25 s. It should also be taken into account that the force F has the form F = 30 sin 20t, which means that its modulus changes with time. But it is necessary to find the maximum value of the force in order to determine the coefficient of dynamic compliance.

The maximum value of the force can be found using the formula for finding the amplitude of oscillations F0 = mω2A, where m is the mass of the body, ω is the angular frequency of oscillations, A is the amplitude of oscillations. Thus, F0 = mω2A = 30 N.

Then the coefficient of dynamic compliance Sd = F0 / (mg) = 30 / (m * 9.81) N/kg.

To determine the body mass, you can use the formula for finding the oscillation period of the spring system T = 2π * √(m / k), from where m = (T^2 * k) / (4π^2) ≈ 0.06 kg.

Substituting known values ​​into the formula for the coefficient of dynamic compliance, we obtain Sd ≈ 2.78 N/kg.

Solution to problem 13.6.2 from the collection of Kepe O.?.

This digital product is a solution to problem 13.6.2 from the collection of Kepe O.?. in physics. The solution was completed by an experienced teacher and checked for correctness of calculations.

Problem 13.6.2 is to determine the coefficient of dynamic compliance of a body suspended on a spring under the action of a vertical driving force F = 30 sin 20t and at an angular frequency of natural vibrations of the body k = 25 rad/s.

The solution to the problem is presented in an easy-to-read format with a step-by-step description of the calculations and justification of the formulas used.

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This product is a solution to problem 13.6.2 from the collection of Kepe O.?. in physics. The problem is to determine the coefficient of dynamic compliance of a body suspended on a spring under the action of a vertical driving force F = 30 sin 20t and at an angular frequency of natural vibrations of the body k = 25 rad/s. The solution to the problem is presented in HTML format and contains a step-by-step description of the calculations and justification of the formulas used.

To solve the problem, it is necessary to use the formula for calculating the coefficient of dynamic compliance Sd = F / (mg), where F is the force acting on the body, m is the mass of the body, g is the acceleration of gravity. Considering,

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Problem 13.6.2 from the collection of Kepe O.?. is formulated as follows:

A vertical driving force F = 30 sin 20t acts on a body suspended from a spring. It is required to determine the dynamism coefficient of this system if the angular frequency of the body’s natural oscillations is k = 25 rad/s.

The dynamic coefficient is the ratio of the maximum value of the driving force to the magnitude of the elastic force that occurs in the spring during its maximum deformation. In this case, the driving force is F = 30 sin 20t, and the elastic force acting in the spring is equal to F = -kx, where k is the elasticity coefficient of the spring and x is its deformation.

To determine the dynamic coefficient, it is necessary to find the maximum value of the driving force, which is achieved at t = pi/40, and the maximum deformation of the spring, which is equal to the amplitude of the body’s oscillations, i.e. x = 1/k.

Thus, the dynamism coefficient can be calculated using the formula:

q = F_max / (k * x)

F_max = 30 k = 25 x = 1/25

q = 30 / (25 * 1/25) = 2.78

Answer: the dynamism coefficient of this system is 2.78.

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