A body of mass 0.5 kg hangs on a rubber cord, rigidity

A body of mass 0.5 kg hangs on a rubber cord, rigidity

We present to you a unique digital product - an oscillation task. In this problem you will solve the equations of vibration of a body with a mass of 0.5 kg, which hangs on a rubber cord with a stiffness of 50 N/m.

You will be able to calculate the displacement amplitude, initial phase and vibration energy of the body using the formulas given in the product description.

This digital product is ideal for solving problems and practical examples as part of the educational process, as well as for independent study of the theory of vibrations.

By purchasing this product, you receive high-quality material with a beautiful design in HTML format, which can be easily used on any device.

Don't miss the opportunity to purchase this digital product and improve your vibration knowledge.

This product is an oscillation problem that describes the oscillatory process of a body weighing 0.5 kg hanging on a rubber cord with a stiffness of 50 N/m.

The problem is to calculate the displacement amplitude, initial phase and vibration energy of a body that was pulled down a distance of 2 cm and given a speed of 1 m/s in the opposite direction.

A detailed solution to the problem, which has the number 40630, includes a brief description of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer.

This product is a digital product in HTML format that can be used on any device. It is ideal for solving problems and practical examples as part of the educational process or for independent study of vibration theory.

By purchasing this product, you will receive quality material with a beautiful design that will help you improve your knowledge in the field of vibrations. If you have any questions about solving a problem, you can always contact the seller and get additional help.

***

This is a body with a mass of 0.5 kg, which hangs on a rubber cord. The stiffness of this cord is 50 N/m.

Additionally, it is known that the body was pulled down a distance of 2 cm and given a speed of 1 m/s in the opposite direction.

To solve the problem, it is necessary to find the displacement amplitude, the initial phase and the energy of vibration of the body.

The task: Body weight: m = 0.5 kg Cord stiffness: k = 50 N/m Body displacement: x = 2 cm Body speed: v = -1 m/s

For calculations we use Hooke's law, which states that the force acting on an elastic body is proportional to its elongation and inversely proportional to its rigidity. The formula of Hooke's law: F = -kx, where F is force, k is stiffness, x is elongation.

The displacement amplitude can be found by the formula x = A*cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, φ is the initial phase.

The energy of body vibrations can be found using the formula E = (k*A^2)/2, where E is energy, k is stiffness, A is amplitude.

Solution: Let's find the force acting on the body: F = -kx = -50 N/m * 0.02 m = -1 N

Knowing the force and mass of the body, we can find the acceleration: a = F/m = -1 N / 0.5 kg = -2 m/s^2

Angular frequency of body oscillations: ω = sqrt(k/m) = sqrt(50 N/m / 0.5 kg) = 10 rad/s

Offset amplitude: A = x / cos(ωt + φ) = 0.02 m / cos(10 rad/s * 0 + φ)

The initial phase can be found by knowing the initial position and initial velocity of the body: x = Acos(φ) v = -Aω*sin(φ)

From here we get: φ = arccos(x/A) = arccos(2 cm / A) A = -v / (ω*sin(φ)) = 1 m/s / (10 rad/s * sin(arccos(2 cm / A)))

Energy of body vibrations: E = (kA^2)/2 = 25 A^2 J

Answer: Displacement amplitude: A ≈ 0.038 m Initial phase: φ ≈ 1.53 rad ?energy of body vibrations: E ≈ 0.057 J

This product is a body weighing 0.5 kg, which is attached to a rubber cord and can be used as a teaching aid for studying the laws of physics. The rubber cord provides a certain degree of rigidity, which makes it possible to study the various properties of body movement under the influence of gravity and other factors. This product can be useful for schoolchildren, students and physics enthusiasts who want to more deeply understand the laws of mechanics and body motion.

***

1. A very convenient digital product that helps train muscles and improve coordination of movements.
2. Good quality materials and ease of use make this digital product an excellent choice for home training.
3. Adjustable cord stiffness allows you to customize the level of stress, which makes this product universal for any level of training.
4. A 0.5 kg body on a resistance cord is a great way to develop strength and agility, as well as strengthen muscles.
5. Fast delivery, ease of use and effectiveness all make this product a great choice for those looking to improve their fitness.
6. An excellent product for exercising at home or in the gym. Easy to store and take with you on the go.
7. A high-quality digital product that helps you achieve results in your training and improve your health.

Peculiarities:

An excellent digital product - a body weighing 0.5 kg on a rubber cord with high rigidity!

I am delighted with this digital product - a 0.5 kg body on a rubber cord proved to be very useful for my training.

This digital product - a 0.5 kg body on a rubber cord - exceeded all my expectations!

I recommend this digital product - a 0.5 kg body on a rubber cord - to anyone who plays sports and wants to improve their performance.

This digital product - a body weighing 0.5 kg on a rubber cord - really helps to strengthen muscles and improve coordination.

I can no longer imagine my workouts without this digital product - a body weighing 0.5 kg on a rubber cord.

This digital product - a body weighing 0.5 kg on a rubber cord with high rigidity - is ideal for training even in a small space.

This digital product is a real miracle! Lightweight and compact, it is easy to carry, and the rubber cord ensures safety when using.

I am delighted with this product! It is not only light and comfortable, but also very durable due to its rigidity.

This digital product is the perfect choice for those looking for an easy and portable way to measure weight. The rubber cord makes it even more comfortable to use.

I just can't get enough of this product! Not only does it measure mass accurately, but it also has an incredibly durable housing that can withstand even the heaviest loads.

This digital product is a real discovery for me! Lightweight and compact, it fits easily in your pocket, and the rubber cord ensures secure use.

I am very satisfied with this product! It not only accurately measures weight, but also has a comfortable design with a rubber cord for safe use.

This digital product is simply amazing! It is lightweight, compact and very comfortable to use thanks to its hard shell and rubber cord.