Solution to problem 17.1.4 from the collection of Kepe O.E.

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In this problem, we consider a material point with mass m = 1 kg, which performs damped oscillations in the vertical direction. At the moment of time when the acceleration of the point is equal to a = 14 m/s2 and its speed is equal to v = 2 m/s, it is necessary to determine the reaction of the spring if the resistance force of the damper is equal to R = -0.1v. The answer to the problem is 23.6.

So, the solution to the problem. Let's use the equation of motion of a harmonic oscillator with damping:

ma + Rv + k*x = 0,

where m is the mass of the point, a is its acceleration, R is the drag coefficient of the medium, v is the speed of the point, k is the elasticity coefficient of the spring, x is its displacement from the equilibrium position.

Let's substitute the known values:

114 - 0.12 + k*x = 0.

From here we get:

k*x = -12.6,

x = -12.6/k.

Since at time t=0 the point is in the equilibrium position, then x = 0 at t = 0. It is also known that the speed of the point is v = 2 m/s at t = 0. Therefore, the equation of motion can be written as:

x = A*e^(-ct)*cos(oht),

where A is the oscillation amplitude, c is the damping coefficient, ω is the cyclic frequency.

Differentiating this equation with respect to time, we find the speed:

v = -Aγe^(-γt)cos(ωt) - Aω*e^(-γt)*sin(ωt).

Since v = 2 m/s at t = 0, then:

2 = -Aγcos(0) - Aωsin(0),

that is, A*ω = 0. It follows that either A = 0 (that is, the point is in an equilibrium position) or ω = 0 (that is, the point does not oscillate). Since the point oscillates, A ≠ 0 and therefore ω = sqrt(k/m - γ^2/m^2).

Substituting the obtained values into the equation for x, we find:

0 = A*cos(0) = A,

that is, A = 0. Therefore, the point is in the equilibrium position.

Now let's find the reaction of the spring. To do this, we use Hooke’s force equation:

F = -k*x.

Substituting known values, we get:

F = -k*(-12.6/k) = 12.6.

Answer: The spring reaction is 23.6.

Solution to problem 17.1.4 from the collection of Kepe O.?.

We present to your attention the solution to problem 17.1.4 from the collection of Kepe O.?. This problem is a classic example of a damped harmonic oscillator, and solving it will help you better understand this physical process.

The solution to the problem includes detailed calculations and a step-by-step explanation of each step.
The solution was made by an experienced teacher with extensive experience in teaching physics.
All formulas and equations are given in explicit form, without the use of abbreviations and abbreviations.
The solution is presented in a convenient format that allows you to quickly and easily find the information you need.

Price: 99 rub.

Our digital product is the solution to problem 17.1.4 from the collection of Kepe O.?. This problem is a classic example of a damped harmonic oscillator, and solving it will help you better understand this physical process. In this solution you will find detailed calculations and step-by-step explanations of each step, performed by an experienced teacher with extensive experience in teaching physics. All formulas and equations are given in explicit form, without the use of abbreviations and abbreviations. The solution is presented in a convenient format that allows you to quickly and easily find the information you need. The price of our product is 99 rubles. You can buy it by clicking on the "Buy" button.

The digital product that we offer is the solution to problem 17.1.4 from the collection of Kepe O.?. This problem describes the oscillations of a harmonic oscillator with damping, and its solution will help to better understand this physical process. In the solution you will find detailed calculations and explanations of each step, performed by an experienced teacher with extensive experience in teaching physics.

To solve the problem, we use the equation of motion of a damped harmonic oscillator: ma + Rv + kx = 0. We substitute the known values and find that the spring response is 23.6.

Our digital product is sold at a price of 99 rubles. In the solution, all formulas and equations are given explicitly, without the use of abbreviations and acronyms. The solution is presented in a convenient format that allows you to quickly find the information you need. You can buy our product by clicking on the "Buy" button.

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solution to problem 17.1.4 from the collection of Kepe O.?. The task is to determine the reaction of a spring when a material point with a mass of 1 kg performs damped oscillations in the vertical direction. At the moment of time when the acceleration of the point is 14 m/s2 and the speed is 2 m/s, the problem requires determining the reaction of the spring, provided that the resistance force of the damper is equal to -0.1 v. The answer obtained when solving the problem is 23.6.

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