Solution to problem 13.4.22 from the collection of Kepe O.E.

13.4.22

The equation of oscillation of a material point is given: x = 20 cos 4t + 30 sin 4t, where x is expressed in cm. It is necessary to determine the amplitude of oscillations in cm.

The amplitude of oscillations is the maximum value of the displacement of a material point from its equilibrium position. To determine the amplitude, it is necessary to find the root of the sum of the squares of the coefficients for sine and cosine:

A = √(20² + 30²) ≈ 36.1 (cm).

Thus, the vibration amplitude is 36.1 cm.

The vibrations of a material point are described by the equation x = 20 cos 4t + 30 sin 4t, where x is expressed in centimeters. To determine the amplitude of oscillations, it is necessary to find the maximum value of the displacement of the point from the equilibrium position. To do this, find the root of the sum of the squares of the coefficients for sine and cosine. We get: A = √(20² + 30²) ≈ 36.1 (cm). Therefore, the vibration amplitude is 36.1 cm.

Solution to problem 13.4.22 from the collection of Kepe O.?.

We present to your attention the solution to problem 13.4.22 from the collection of problems by Kepe O.?. The solution is presented in the format of a digital product, which allows you to receive it instantly and start using it without delay.

In this problem, it is necessary to determine the amplitude of oscillations of a material point given by the equation x = 20 cos 4t + 30 sin 4t in centimeters. The solution to this problem is presented in a convenient format with a step-by-step description of the solution and detailed calculations.

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This product is a solution to problem 13.4.22 from the collection of problems by Kepe O.?. in the format of a digital product. In the problem, it is necessary to determine the amplitude of oscillations of a material point given by the equation x = 20 cos 4t + 30 sin 4t in centimeters. The solution is presented in a convenient format with a step-by-step description of the solution and detailed calculations.

By purchasing this product, you receive a complete and detailed solution to the problem, a convenient format for presenting the material, quick access to the solution without having to wait for delivery, high quality information and the ability to use the solution as an example for solving similar problems yourself.

Answer to the problem: the amplitude of vibration is 36.1 cm.

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For problem 13.4.22 from the collection of Kepe O.?. the equation of vibration of a material point is given: x = 20 cos 4t + 30 sin 4t, where x is measured in centimeters.

It is necessary to determine the amplitude of vibrations in centimeters.

The amplitude of oscillations is the maximum displacement of a material point from its equilibrium position. In this case, since the oscillation is specified as the sum of sine and cosine, we can use the formula to find the amplitude of the oscillations:

A = √(a^2 + b^2),

where a and b are the coefficients for sine and cosine, respectively.

In our case a = 30, b = 20, so

A = √(30^2 + 20^2) = √(900 + 400) = √1300 ≈ 36.1 cm.

Thus, the vibration amplitude is 36.1 cm.

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