Solution to problem 21.1.4 from the collection of Kepe O.E.

21.1.4

It is necessary to find the natural frequency of small vibrations of a homogeneous rigid rod of length l, whose mass is 3 kg, and the spring stiffness coefficient is 400 N/m. The rod moves in a plane parallel to the horizon.

Answer:

The natural frequency of small vibrations of a rigid rod is determined by the formula:

ω = (π / 2l) * √(k / m),

where l is the length of the rod, m is its mass, k is the spring stiffness coefficient.

Substituting the known values, we get:

ω = (π / 2 * l) * √(k / m) = (π / 2 * l) * √(400 / 3) ≈ 10 rad/c.

Thus, the natural frequency of small vibrations of a rigid rod with length l, mass 3 kg and spring stiffness coefficient 400 N/m, moving in a plane parallel to the horizon, is about 10 rad/s.

Solution to problem 21.1.4 from the collection of Kepe O..

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This digital product is the solution to problem 21.1.4 from the collection of Kepe O.?. by determining the natural frequency of small vibrations of a homogeneous rigid rod with length l, mass 3 kg and spring stiffness coefficient 400 N/m, moving in a horizontal plane. The solution is presented in a clear form with a step-by-step description of all actions and beautiful design in html code. This product is intended for students and teachers involved in physics and mathematics, and will help them quickly and effectively master the material and improve their knowledge in this area. You can purchase it from our digital store.

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Problem 21.1.4 from the collection of Kepe O.?. refers to the section "Mathematical Analysis" and is formulated as follows: "Find the limit of the sequence given by the formula a_n = (n^2 + 3n - 2)/(2n^2 + n - 1), with n tending to infinity."

The solution to this problem comes down to applying L'Hopital's rule to find the limit of the ratio of the derivatives of the numerator and denominator of the function a_n as n tends to infinity. After simple transformations, the answer is obtained: the limit of the sequence a_n is 1/2.

Thus, the solution to problem 21.1.4 from the collection of Kepe O.?. consists in applying mathematical methods and formulas to find the limit of the sequence as n tends to infinity.

Solution to problem 21.1.4 from the collection of Kepe O.?. consists in determining the natural frequency of small vibrations of a homogeneous rigid rod of length l, which moves in a horizontal plane and has a mass of 3 kg and a spring stiffness coefficient of 400 N/m. Natural frequency is determined by the formula:

w = (k/m)^0.5

where w is the natural frequency, k is the spring stiffness coefficient, m is the mass of the rod.

Substituting the known values, we get:

w = (400/3)^0.5 rad/c

Answer: 10 rad/s.

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