Problem 15.2.2 from the collection of Kepe O.?. (2005 edition) is formulated as follows:
“At ground level, a pendulum 1 m long swings with a period of 2 s. Determine the speed and acceleration of the pendulum at the moment of time when its potential energy is equal to its kinetic energy.”
This problem is solved by expressing the speed and acceleration of the pendulum through its coordinates and initial conditions of motion. First, you need to determine the amplitude of the pendulum's oscillations using the known period value and the formula for the oscillation period. Then you should find the position of the pendulum at the moment of time when its potential energy is equal to its kinetic energy. To do this, you can use the law of conservation of mechanical energy. Next, using formulas for expressing speed and acceleration through the coordinates of the pendulum and its initial conditions of motion, you can find the required values.
The solution to this problem can be useful for students studying mechanics, physics and other natural science disciplines.
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Problem 15.2.2 from the collection of Kepe O.?. refers to the field of mathematical analysis and consists of finding a definite integral. In particular, you need to calculate the integral of a function given by a formula over a certain interval. Solving the problem involves a sequence of mathematical transformations, including replacing a variable, bringing the integrand to a more convenient form, applying integration formulas, and calculating the value of the integral. The solution to the problem can be used for practical calculations in various fields of science and technology, for example, in physics, economics and engineering.
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