Solution to problem 21.1.1 from the collection of Kepe O.E.

21.1.1 In a given mechanical system, small vibrations can be described by the differential equation q + (4π)2q = 0, where q - represents the generalized coordinate, m. The initial displacement of the system is q0 = 0.02 m, and the initial speed qo = 2 m /With. It is necessary to determine the amplitude of oscillations. The solution to this equation will be q = q0cos(2πt/T), where T is the oscillation period. The amplitude of the oscillations can be calculated as A = |q0| = 0.02 * |cos(2πt/T)|. Substituting the initial conditions, we obtain A = 0.02 m * |cos(0)| = 0.02 m * 1 = 0.02 m. However, this value represents the maximum value of the vibration amplitude. Since q = q0cos(2πt/T), the minimum amplitude value will be equal to |q0| = 0.02 m * |cos(π)| = 0.02 m * (-1) = -0.02 m. Therefore, the amplitude of vibration is 0.02 m - (-0.02 m) = 0.04 m. Answer: 0.160 m.

Solution to problem 21.1.1 from the collection of Kepe O.?.

We present to your attention the solution to problem 21.1.1 from the collection “Problems in General Physics” by the author Kepe O.?. This digital product is an ideal solution for students and teachers who are looking for quality material to prepare for exams or to improve their knowledge in the field of physics.

This digital product includes a detailed solution to Problem 21.1.1, which describes small vibrations of a mechanical system using a differential equation. The solution to the problem is presented in a clear and easily accessible form, which allows you to quickly and efficiently learn the material.

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This product is a solution to problem 21.1.1 from the collection “Problems in General Physics” by the author Kepe O.?.

The problem describes a mechanical system for which small vibrations can be described by the differential equation q + (4π)2q = 0, where q is a generalized coordinate, m. The initial conditions are given: q0 = 0.02 m and qo = 2 m/s. It is necessary to determine the amplitude of oscillations.

The solution to the problem is presented in the form of formulas and calculations that allow you to determine the amplitude of the oscillations. The solution results in an answer of 0.160 m.

Purchasing this digital product allows you to receive a detailed solution to the problem, presented in a clear and easily accessible form. You can also use the solution to study for exams or improve your knowledge of physics.

This product is a solution to problem 21.1.1 from the collection "Problems in General Physics" by the author Kepe O.?. The problem describes small vibrations of a mechanical system using a differential equation. The product includes a detailed solution to the problem in a clear and easily accessible form, which allows you to quickly and efficiently learn the material. The amplitude of the system oscillations is determined based on the given initial conditions: initial displacement q0 = 0.02 m and initial speed qo = 2 m/s. The solution to the equation is q = q0cos(2πt/T), where T is the oscillation period. The amplitude of oscillations is defined as A = |q0|, where |q0| - maximum value of function q. Substituting the initial conditions, we get A = 0.04 m. The product is intended for students and teachers who are looking for quality material to prepare for exams or to improve their knowledge in the field of physics. By purchasing this product, you get convenient and quick access to the material at any time and from anywhere.

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Solution to problem 21.1.1 from the collection of Kepe O.?. consists in determining the amplitude of oscillations of a mechanical system, described by the differential equation q + (4π)²q = 0, where q is the generalized coordinate, m.

Initial conditions of the problem: initial displacement of the system q₀ = 0.02 m and initial speed q₀' = 2 m/s.

To find the amplitude of oscillations, it is necessary to solve this differential equation. The general solution of such an equation has the form q(t) = Acos(2πt) + Bsin(2πt), where A and B are arbitrary constants determined by the initial conditions.

Using the initial conditions q₀ = 0.02 m and q₀' = 2 m/s, we can write the system of equations:

q(0) = Acos(0) + Bsin(0) = A = 0,02 м q'(0) = -2πAsin(0) + 2πBcos(0) = 2 m/s

From here we find B = 0.16 m, which means the oscillation amplitude is equal to |A + iB| = sqrt(A² + B²) = 0.16 m.

Thus, the solution to the problem is to determine the vibration amplitude of the mechanical system, which is 0.16 m.

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