Newton Method of Numerical - Free Undamped Single Degree of Freedom Vibration System

TL;DR

This video explains the equation of vibration for a water column in YouTube using the Newton method.

Transcript

hello everyone in this video we'll discuss a numerical using the newton method so we know that the newton method is based on the loss of motions of newton so in this question we have to find the equation of vibration for the water column in youtube so we say that in a youtube if there is some water column so we say that the density let's say the de... Read More

Key Insights

• ❓ The Newton method can be used to derive equations of motion for various systems.
• 💦 The equation of vibration for a water column in YouTube is derived by considering the external force and inertia force.
• ☺️ The total rise or fall of the water column is determined by the term 2g * x / l.
• 💦 The Newton method is used to solve the derived equation and find the natural frequency of the water column.

Questions & Answers

Q: How is the equation of vibration for a water column in YouTube derived?

The equation is derived by considering the total force on the system, which is the external force applied and the restoring force or inertia force. By using Newton's second law and considering the mass and acceleration, the equation is obtained.

Q: What is the significance of the term 2g * x / l in the equation?

The term represents the total rise or fall of the water column in response to the applied force. It accounts for the potential energy gained by the water column when it rises and the restoring force due to gravity that brings it back to the equilibrium position.

Q: How does the Newton method relate to the equation of vibration?

The Newton method is used to solve the equation of vibration and find the natural frequency of the water column. By comparing the derived equation with the general equation of Simple Harmonic Motion (SHM), the natural frequency of the water column is determined to be sqrt(2g/l).

Q: What factors affect the natural frequency of the water column?

The natural frequency of the water column depends on the acceleration due to gravity (g) and the length of the column (l). As these values change, the natural frequency will also change.

Summary & Key Takeaways

• The Newton method is based on the laws of motion by Newton.

• The equation of vibration for a water column in YouTube is derived by considering the external force applied and the restoring force.

• The equation is found to be acceleration + 2g * x / l = 0, where g is acceleration due to gravity.