Solution to problem 13.4.11 from the collection of Kepe O.E.

13.4.11 A body is suspended from a spring and performs free vertical oscillations with a period T = 0.5 s. Determine the mass of the point if the spring stiffness coefficient c = 200 N/m (Answer 1.27)

Given: oscillation period T = 0.5 s, spring stiffness coefficient c = 200 N/m. Let's find the mass of a point suspended on a spring.

The period of oscillation of a mathematical pendulum is related to its length L and the acceleration of gravity g as follows: T = 2π√(L/g). For a spring whose stiffness is c, the period of oscillation is related to its mass m and the constant of proportionality c as follows: T = 2π√(m/c).

Comparing these two expressions, we get: √(m/c) = √(L/g), or m = c(L/g). Substituting numerical values, we get: m = 200(0.5/9.81) ≈ 1.27 kg.

Answer: 1.27.

Solution to problem 13.4.11 from the collection of Kepe O.?.

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This digital product is a solution to problem 13.4.11 from the collection of Kepe O.?. in physics. The problem is to determine the mass of a point suspended on a spring, which performs free vertical oscillations with a period T = 0.5 s with a spring stiffness coefficient c = 200 N/m.

The solution contains all the necessary formulas, explanations and calculations necessary to solve the problem. The solution is designed in a beautiful html style, which makes it convenient and easy to read.

By purchasing this digital product, you get access to a high-quality solution to the problem that will help you better understand the material and prepare for the physics exam. In addition, you save your time by avoiding the need to solve the problem yourself and search for the necessary information.

The answer to the problem is 1.27 kg and is also presented in the solution. Don't miss the opportunity to purchase this digital product and get a high-quality solution to problem 13.4.11 from the collection of Kepe O.?. right now!

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Solution to problem 13.4.11 from the collection of Kepe O.?. consists in determining the mass of a point that is suspended from a spring and performs free vertical oscillations with a period of T = 0.5 s.

To solve the problem, it is necessary to use the formula for the period of oscillation of a body on a spring:

T = 2π√(m/s)

where T is the oscillation period, m is the body mass, s is the spring stiffness coefficient.

By rearranging the formula, we can express the body mass m:

m = (T^2 * с) / (4π^2)

Substituting known values, we get:

m = (0.5^2 * 200) / (4π^2) ≈ 1.27

Thus, the mass of a point suspended from a spring and performing free vertical oscillations with a period T = 0.5 s with a spring stiffness coefficient c = 200 N/m is equal to 1.27 kg.

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