# Centre of mass vs oscillation

• MathewsMD

#### MathewsMD

My original question was answered, but I would just like some clarification regarding one concept. In the derivation for the centre of percussion in this link (http://en.wikipedia.org/wiki/Center_of_percussion), what exactly is the variable A? How can it be determined (theoretically and/or experimentally)?

Last edited:
Symmetry777
Symmetry777
A.T. said:
As the article says, distance from pivot to center of mass.

Ahh thank you. For some reason I just could not see it.

At the bottom of that section, it states: "This is also the center of oscillation of a physical pendulum of the same mass M, hung at the pivot point. (The center of oscillation is the position of the mass of a simple pendulum that has the same period as the physical pendulum.)[2]"

Does the article prove this at all? Maybe I'm missing something here, but is that statement an easily seen corollary? I can show it is true for single examples, but is there a proof for the general case?

Symmetry777

## 1. What is the centre of mass?

The centre of mass is the point at which the entire mass of a body can be considered to be concentrated. It is the point around which an object's weight is evenly distributed, and it is also the point at which the object would balance if it were placed on a pivot.

## 2. How is the centre of mass calculated?

The centre of mass can be calculated by finding the weighted average of the individual masses and their positions in space. This can be done using the formula: xcm = (∑mixi) / (∑mi), where xcm is the x-coordinate of the centre of mass, mi is the mass of each individual component, and xi is the x-coordinate of each individual component.

## 3. What is oscillation?

Oscillation is a repetitive back and forth motion around an equilibrium point. It occurs when a system is displaced from its equilibrium and then allowed to return to its original position. Examples of oscillation include a pendulum swinging back and forth and a mass on a spring bouncing up and down.

## 4. How are the centre of mass and oscillation related?

The centre of mass and oscillation are related because the centre of mass is the point around which an object will oscillate if it is allowed to do so. In other words, the centre of mass is the point of equilibrium for an object in oscillation. Additionally, the motion of the centre of mass can be used to analyze the overall motion of an oscillating system.

## 5. How does the centre of mass affect the stability of an oscillating system?

The centre of mass plays a crucial role in the stability of an oscillating system. If the centre of mass is located above the pivot point of the system, it will result in a stable oscillation. However, if the centre of mass is below the pivot point, the system will be unstable and may topple over. This is why it is important to consider the centre of mass when designing and analyzing oscillating systems.