Solution to problem 13.4.20 from the collection of Kepe O.E.

13.4.20 In the problem, a body of mass m = 0.3 kg is given, which is suspended from a spring and performs free vertical oscillations with an amplitude of 0.4 m. The initial position of the body coincides with the position of static equilibrium, and the initial speed is 3 m/s. It is necessary to determine the spring stiffness coefficient.

To solve the problem, you can use the formula for the period of oscillation of a body on a spring:

T = 2π √(m/k),

where T is the oscillation period, m is the body mass, k is the spring stiffness coefficient.

From the problem conditions it is known that the oscillation amplitude is 0.4 m and the initial speed is 3 m/s. It is also known that the oscillations began from a position of static equilibrium, which means that at the initial moment of time the potential energy of the body was maximum and kinetic energy was minimum.

Using the law of conservation of energy, we can express the spring stiffness coefficient:

mgA^2/2 = kA^2/2 + mv^2/2,

where g is the acceleration of gravity, A is the amplitude of oscillations, v is the initial speed.

Solving this equation for k, we get:

k = mg/(A^2) - v^2/(A^2) = 0,3*9,81/(0,4^2) - 3^2/(0,4^2) ≈ 16,9

Thus the spring constant is about 16.9.

Solution to problem 13.4.20 from the collection of Kepe O.?.

Our digital product is the solution to problem 13.4.20 from the collection of Kepe O.?. in physics. The solution was completed by a professional teacher and presented in the form of an electronic document.

The task is to determine the spring stiffness coefficient during free vertical oscillations of a body weighing 0.3 kg with an initial speed of 3 m/s and an amplitude of 0.4 m.

Our solution is based on the application of the formula for the period of oscillation of a body on a spring and the law of conservation of energy. The result is a precise spring constant value of about 16.9.

By purchasing our digital product, you receive a ready-made solution to the problem, which can be used for educational or scientific purposes. Beautiful html document design makes it easy to read and use.

Our digital product is the solution to problem 13.4.20 from the collection of Kepe O.?. in physics. The problem gives a body with a mass of 0.3 kg, suspended from a spring, which performs free vertical oscillations with an amplitude of 0.4 m. It is necessary to determine the stiffness coefficient of the spring if the oscillations began from a position of static equilibrium with an initial speed of 3 m/s. The solution to the problem is based on the application of the formula for the period of oscillation of a body on a spring and the law of conservation of energy.

In our solution, we used the formula for the period of oscillation of a body on a spring: T = 2π √(m/k), where T is the period of oscillation, m is the mass of the body, k is the spring stiffness coefficient. From the problem conditions it is known that the oscillation amplitude is 0.4 m and the initial speed is 3 m/s. It is also known that the oscillations began from a position of static equilibrium, which means that at the initial moment of time the potential energy of the body was maximum and kinetic energy was minimum. Using the law of conservation of energy, we expressed the spring stiffness coefficient: mgA^2/2 = kA^2/2 + mv^2/2, where g is the acceleration of gravity, A is the amplitude of oscillations, v is the initial velocity.

Solving this equation for k, we found that the spring constant is about 16.9. Our solution is presented in the form of an electronic document with a beautiful HTML design, which makes it easy to read and use. By purchasing our digital product, you receive a ready-made solution to the problem, which can be used for educational or scientific purposes.

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Here is the solution to problem 13.4.20 from the collection of Kepe O.?.:

Given: body weight, m ​​= 0.3 kg vibration amplitude, A = 0.4 m initial speed, v = 3 m/s you need to find the spring stiffness coefficient, k.

Solution: The period of oscillation of a body on a spring can be expressed through the spring stiffness coefficient and the mass of the body: T = 2π√(m/k)

The amplitude of oscillations is related to the initial speed as follows: A = v/(ω√(1 - (v/ωA)^2))

where ω = 2π/T is the cyclic oscillation frequency.

Substituting the expression for T from the first equation into the second and solving for k, we get: k = mω^2 = 4π^2m/T^2

Substituting the data from the problem statement, we get: T = 2π√(m/k) = 2π√(0.3/k)

A = v/(ω√(1 - (v/ωA)^2)) = 0.4 m

Solving the equation for k, we get: k = (4π^2m)/T^2 = (4π^2m)/(4π^2(0.3/k)) = 16.9 N/m

Answer: spring constant, k = 16.9 N/m.

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