Solution to problem 13.6.4 from the collection of Kepe O.E.

13.6.4 Static elongation of the spring under the action of a load λ = 9.81 cm.

It is necessary to determine the dynamic coefficient if a vertical driving force F = 15 sin 5t acts on the load.

Answer:

The dynamism coefficient is determined by the formula:

k_d = (F_max - F_min)/min

where F_max and F_min - maximum and minimum values ​​of force F, respectively.

The periodic driving force has the form:

F = F₀ sin ωt

where F₀ - force amplitude, ω - cyclic frequency.

Then the maximum and minimum force values ​​can be expressed as follows:

F_max = F₀, F_min = -F₀

Substituting the values ​​into the formula for the dynamic coefficient, we get:

k_d = (F_max - F_min)/min = (F₀ + F₀)/λ =2F₀/λ

Thus, to find the dynamic coefficient, it is necessary to find the amplitude of the force F and substitute it into the formula along with the known value of λ:

F₀ = 15, ω = 5 с^-1, λ = 9.81 cm = 0.0981 m.

Then:

k_d = 2F₀/λ = 2*15/0.0981 ≈ 305,9

The dynamic coefficient shows how strongly the spring reacts to changes in external force. The larger the coefficient, the more strongly the spring reacts to changes in external force. In this case, the dynamic coefficient is 305.9, which indicates that the spring reacts very strongly to changes in external force.

Solution to problem 13.6.4 from the collection of Kepe O.?.

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The digital product that is offered contains the solution to problem 13.6.4 from the collection "Problems in General Physics" by Kepe O.?. In this problem, it is necessary to find the dynamic coefficient of a spring that is subject to static elongation under the action of a load, in the presence of a vertical driving force F = 15 sin 5t.

Solving the problem occurs in several steps. First, it is necessary to express the maximum and minimum values ​​of the force F using the periodic law of change of this force. Then, using the formula for the dynamism coefficient, the value of this coefficient is calculated, substituting known values.

The digital product contains an accurate and understandable description of the problem conditions, a detailed solution with a step-by-step explanation of each action, illustrations and graphs that help to better understand the solution to the problem, as well as an answer to the problem with justification for each step of the solution.

This digital product can be useful for anyone studying physics who wants to better understand the topic of spring dynamic coefficient. It can be used as a study guide or to prepare for exams. In addition, the product guarantees quality and full compliance with the original text of the problem.

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Problem book Kepe O.?. contains many problems on various topics in physics, including problem 13.6.4, which is devoted to the static elongation of a spring under the action of a load.

In this problem, it is necessary to determine the dynamic coefficient of the spring under the action of a vertical driving force F = 15 sin 5t and static elongation λ = 9.81 cm. The dynamic coefficient is the ratio of the amplitude of oscillations of the spring to the inductance of the load, i.e. to the mass associated with the load.

To solve the problem, it is necessary to use the equation of oscillations of a spring pendulum and express the dynamism coefficient in terms of known quantities. After substituting numerical values ​​and solving the equation, you can get the answer equal to 1.33.

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