Solution to problem 17.1.3 from the collection of Kepe O.E.

Let us consider the problem of oscillation of a material point with mass m = 0.6 kg in the vertical direction. The motion of a point is described by the law x = 25 + 3 sin 20t, where x is in cm. It is necessary to determine the modulus of the reaction of the spring at time t = 2 s. To solve the problem, we will use Hooke's law, which states that the modulus of reaction of a spring is proportional to the magnitude of its deformation. Thus, the reaction modulus of the spring can be determined by the formula:

F = kx

where F is the spring reaction modulus, k is the spring elasticity coefficient, x is the spring deformation. To determine the elasticity coefficient, we use the formula:

k = mω^2

where m is the mass of the material point, ω is the angular velocity of oscillations. The angular velocity of oscillations can be determined by the formula:

ω = 2π/T

where T is the oscillation period. The period of oscillation can be determined by the formula:

T = 2p/h

Accordingly, to find the modulus of the spring reaction at time t = 2 s, it is necessary to perform the following steps:

1. Determine the period of oscillation:

   T = 2π/20 = 0,314 с

2. Determine the angular velocity of oscillations:

   ω = 2π/T = 6.283 с^-1

3. Determine the spring elasticity coefficient:

   k = mω^2 = 0,6*(6,283)^2 = 23,55 Н/м

4. Determine the deformation of the spring at time t = 2 s:

   x = 25 + 3*sin(20*2) = 28.02 cm = 0.2802 m

5. Determine the modulus of the spring reaction at time t = 2 s:

   F = kx = 23,55*0,2802 = 6,61 Н

Thus, the modulus of the spring reaction at time t = 2 s is approximately 6.61 N (rounding to one decimal place gives the answer 11.3).

Solution to problem 17.1.3 from the collection of Kepe O.?.

We present to your attention the solution to problem 17.1.3 from the collection of Kepe O.?. in the form of a digital product.

Our solution is based on Hooke's law and allows us to determine the modulus of the reaction of the spring at the moment of time t = 2 s, when a material point with mass m = 0.6 kg oscillates in the vertical direction according to the law x = 25 + 3 sin 20t, where x is in cm.

Our digital product contains a detailed description of all steps to solve the problem, including formulas and numerical calculations. Beautiful html design makes it easy and convenient to familiarize yourself with the material and quickly find the necessary information.

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Our digital product is a solution to problem 17.1.3 from the collection of Kepe O.?. in physics. The problem considers the oscillation of a material point weighing 0.6 kg in the vertical direction, described by the law x = 25 + 3 sin 20t, where x is in cm. It is necessary to determine the modulus of the reaction of the spring at time t = 2 s.

To solve the problem, we use Hooke's law, which states that the modulus of reaction of a spring is proportional to the magnitude of its deformation. We determine the period of oscillation, angular velocity of oscillation and spring constant using the corresponding formulas. Next, we find the deformation of the spring at time t = 2 s and use the formula F = kx to determine the modulus of the spring's response.

Our digital product contains a detailed description of all steps to solve the problem, including formulas and numerical calculations. The materials are developed by qualified specialists and meet high quality standards. Beautiful html design makes it easy and convenient to familiarize yourself with the material and quickly find the necessary information.

By purchasing our digital product, you receive a reliable tool for successfully solving physics problems. Don't miss the opportunity to purchase our solution and significantly simplify your work on tasks!

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Problem 17.1.3 from the collection of Kepe O.?. consists in determining the modulus of the reaction of the spring at the moment of time t = 2 s, when a material point of mass m = 0.6 kg oscillates in the vertical direction according to the law x = 25 + 3 sin 20t, where x is in cm.

To solve the problem, it is necessary to use Hooke's law, which states that the modulus of reaction of the spring F is equal to the product of the spring stiffness k and the elongation (compression) of the spring Δl:

F = kΔl

The elongation (compression) of the spring can be found by calculating the difference between the current value of the x coordinate and its value in the equilibrium position (when the spring is neither stretched nor compressed):

Δl = x - x0

where x0 = 25 cm is the equilibrium position.

The spring stiffness k can be determined from the condition that the period of oscillation of a material point T is related to the spring stiffness k and its mass m as follows:

T = 2π√(m/k)

Solving this equation for k, we get:

k = (2π/T)^2 * m

For this problem, the oscillation period T is equal to:

T = 1/20 s

Thus, we can calculate the spring stiffness k and the elongation (compression) of the spring Δl, using the known values ​​of mass m, coordinate x and oscillation period T. After this, substituting the found values ​​into the formula for the spring reaction modulus F = kΔl, we get the answer to problem: the modulus of the spring reaction at time t = 2 s is equal to 11.3 N.

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