# About the formula of pendulum -- What if there is damping?

• karimce
In summary, the conversation on the Physics Stack Exchange was discussing the formula for a pendulum's angle, which had a constant curve and needed to be corrected to have a decreasing curve. The user was seeking assistance in finding a suitable equation, and the suggestion was to look into the damped harmonic oscillator.
karimce

a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]

a(t) : the angle in instant t .
t : time
g : gravity .
Pi = 3.14
k = Fixed (Friction )
l : longer of pendulum

but this formula is wrong , because the curve of this formula Remains constant , like this :

I want to correct this equation to become true Means keeps decreasing curve, even non-existent ( = 0 ) .

Specifically I want to change in the second part , in [ k/(m*l*l) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]

can you help me ? Are there any other equation?

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## 1. How does damping affect the movement of a pendulum?

Damping is the process in which energy is dissipated from a system, causing it to slow down or lose amplitude. In the case of a pendulum, damping can cause the pendulum to swing with decreasing amplitude over time, resulting in shorter and slower swings.

## 2. Can damping be beneficial for a pendulum?

In some cases, damping can be beneficial for a pendulum. If the pendulum is used for timekeeping, damping can help regulate the pendulum's movement and make it more accurate. Damping can also be useful in preventing the pendulum from swinging too wildly, which can damage the pendulum or its surroundings.

## 3. How does the formula for a damped pendulum differ from an undamped one?

The formula for a damped pendulum includes an additional term for damping, which takes into account the energy lost due to damping. This term is typically represented by a damping coefficient, which is dependent on the properties of the pendulum and the medium in which it is swinging.

## 4. Is it possible to eliminate damping in a pendulum?

In theory, it is possible to eliminate damping in a pendulum by placing it in a vacuum, where there is no medium to dissipate energy. However, in practical applications, damping is always present to some degree and cannot be entirely eliminated.

## 5. How does the length of a pendulum affect damping?

The length of a pendulum does not directly affect damping. However, it can indirectly impact damping by affecting the period of the pendulum. A longer pendulum will have a longer period, which means it will take longer for the pendulum to complete a full swing, resulting in less damping over time.

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