A particle with mass m = 50 g oscillates, equation

A particle with a mass of m = 50 g oscillates, the equation of which has the form x = Acoswt, where A = 10 cm and w = 5 c^-1. Find the force Fx acting on the particle at the position of its greatest displacement.

Problem 40464. Detailed solution with a brief record of the conditions, formulas and laws used in the solution, derivation of the calculation formula and answer. If you have any questions regarding the solution, please write. I try to help.

To solve the problem, it is necessary to use Hooke's law, which states that the force acting on a body is proportional to its displacement from the equilibrium position. We will also use the formula to find the period of oscillation of the body: T = 2π/ω.

The period of oscillation of the body is equal to:

T = (2π)/(5 c^-1) = 1.26 c

The maximum displacement of the body is:

x_max = A = 10 cm = 0.1 m

The force acting on the body at the position of its greatest displacement is determined by the formula:

Fx = -k * x_max,

where k is the stiffness coefficient of the spring, which creates vibrations of the body.

The spring stiffness coefficient can be found using the formula:

k = m * ω^2,

where m is the body mass, ω is the angular frequency of oscillations.

Substituting the values ​​of m and ω into the formula for k, we get:

k = 50 g * (5 s^-1)^2 = 1250 g/s^2 = 12.5 N/m

Now we can find the force Fx:

Fx = -k * x_max = -12.5 N/m * 0.1 m = -1.25 N

Answer: Fx = -1.25 N.

Product description

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Product Description: The digital goods store presents a unique digital product for those who are interested in physics and mathematics - “A particle of mass m = 50 g oscillates, equation.” This product contains a detailed description of the solution to problem No. 40464, which is associated with vibrations of a particle weighing 50 g. The solution to the problem includes a brief recording of the conditions, formulas and laws used in the solution, derivation of the calculation formula and the answer.

The product description is presented in a beautiful HTML format, which makes it easy to read and study the material. By purchasing this digital product, you get access to useful material that will help you better understand the basics of physics and mathematics. Don't miss the opportunity to purchase a unique digital product for your education and development!

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This product is a solution to problem 40464, which involves determining the force acting on a particle oscillating.

Problem condition: a particle with a mass m = 50 g oscillates, the equation of which has the form x = Acoswt, where A = 10 cm and w = 5 c^-1. It is necessary to find the force Fx acting on the particle at the position of its greatest displacement.

To solve the problem, Hooke's law is used, which establishes the relationship between force and displacement from the equilibrium position. For harmonic vibrations, the formula Fx = -kx is valid, where k is the spring stiffness coefficient.

Since x = Acoswt, then the maximum displacement is A, and the force Fx at the position of maximum displacement will be equal to Fx = -k*A.

To express the stiffness coefficient k through the information given in the problem, we use the formula for the oscillation period T = 2π/ω, where ω is the circular frequency.

It is known that the oscillation period is T = 1/2 s. Then we can express the circular frequency: ω = 2π/T = 4π s^-1.

The stiffness coefficient k can be found using the formula k = mω^2. Substituting known values, we obtain k = 100π N/m.

So, the force Fx acting on the particle at the position of its greatest displacement is equal to Fx = -k*A = -10π N ≈ -31.42 N.

Thus, the required force is approximately -31.42 N.

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