Solution to problem 13.4.2 from the collection of Kepe O.E.

13.4.2 A load with a mass m = 20 kg is suspended from a spring with a stiffness coefficient c = 400 N/m and is in free linear vertical oscillatory motion. Determine at what distance from the position of static equilibrium is the center of gravity of the load at the moment of time when its acceleration is 3 m/s. (Answer 0.15)

In the problem there is a mass of 20 kg, which is suspended from a spring with a stiffness coefficient of 400 N/m and moves in a free linear vertical oscillatory motion. It is necessary to find the distance from the static equilibrium position at which the center of gravity of the load is located at the moment of time when its acceleration is 3 m/s.

To solve the problem, you can use the oscillation equation:

a = -ω^2x,

where a is the acceleration of the load, ω is the circular frequency of oscillations, x is the displacement of the load from the position of static equilibrium.

Circular frequency ω is related to the spring stiffness coefficient c and the load mass m as follows:

ω = √(с/m).

Substituting the expression for ω into the vibration equation, we obtain:

x = -(a/ω^2) = -(3/((400/20)^0.5)^2) = -0.15 m.

Answer: 0.15 m.

Solution to problem 13.4.2 from the collection of Kepe O.?.

Solution to problem 13.4.2 from the collection of Kepe O.?. is a digital product that represents a mathematical problem from the field of mechanics. This product is intended for students and teachers studying physics.

The problem involves a mass of 20 kg suspended from a spring with a stiffness coefficient of 400 N/m and in free linear vertical oscillatory motion. It is necessary to determine the distance from the static equilibrium position at which the center of gravity of the load is located at the moment of time when its acceleration is 3 m/s.

The solution to the problem includes formulas, explanations and a detailed description of the solution steps. The product is presented in PDF format and can be downloaded immediately after purchase.

By purchasing this digital product, you receive useful material for studying and preparing for exams. In addition, you save time and money that could have been spent searching for a similar task in other sources.

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Problem 13.4.2 from the collection of Kepe O.?. consists of determining the distance from the position of static equilibrium to the center of gravity of a load weighing 20 kg, which is suspended from a spring with a stiffness coefficient of 400 N/m and is in free linear vertical oscillatory motion. The problem requires determining this distance at the time when the acceleration of the load is 3 m/s. The answer to the problem is 0.15 meters.

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