# How Can Amplitude Decay be Modeled with a Pendulum and Friction Coefficient?

• satori20
In summary, The rate of amplitude decay of a pure tone sine wave can be manipulated with a friction coefficient using a literal physical pendulum modeled with equations and computer simulation. The frequency and length of the pendulum can help determine the decibel level and amplitude of the wave, but not the rate of decay.

#### satori20

Basic premise: a pure tone sine wave can be modeled with a pendulum and the rate of amplitude decay can be manipulated with a friction coefficient.

So... does anyone know how this is actually done? In other words if you picked a pure tone (let's say middle C @ 261.6 Hz) initiated at a certain dB (let's say 50dB), how would you factor in rate of decay and how would you replicate this with a literal physical pendulum?

I know this is a complex question and I'm not even sure anyone is doing this but there's got to be equations and computer modeling that does. Obviously I'm just learning about this so the simplest explanation possible would be wonderful. 1st post here btw, so I hope it's in the right area :) Thanks!

Here's something...

Frequency of a pendulum = $$\frac{1}{2\pi}\sqrt{\frac{g}{L}}$$

The decibel level depends on your distance. The logic would be

Intensity level => intensity => power => energy => amplitude

So this could tell you how far the pendulum moves (if large--which it probably is--it may invalidate the previous formula), but not the rate of decay.

## 1. What is amplitude decay modeling?

Amplitude decay modeling is a scientific approach used to determine the rate at which a signal or wave decreases in amplitude as it travels through a medium or space. It is commonly used in fields such as acoustics, seismology, and telecommunications to predict the weakening of a signal over distance or time.

## 2. How does amplitude decay modeling work?

Amplitude decay modeling involves mathematical calculations based on the characteristics of the medium through which the signal is traveling, such as density, temperature, and composition. These calculations take into account factors such as absorption, scattering, and reflection of the signal in order to estimate the decrease in amplitude.

## 3. What are the applications of amplitude decay modeling?

Amplitude decay modeling is commonly used in various fields, including audio engineering, earthquake monitoring, and signal transmission. It can be used to optimize sound systems, predict the strength of seismic waves, and improve the reliability of communication systems.

## 4. What are the limitations of amplitude decay modeling?

While amplitude decay modeling is a useful tool, it is important to note that it is based on theoretical calculations and may not always accurately represent real-world conditions. Factors such as unpredictable weather patterns, changes in the medium, and interference from other signals can affect the accuracy of the results.

## 5. How is amplitude decay modeling different from other signal propagation models?

Amplitude decay modeling differs from other signal propagation models, such as path loss modeling, in that it specifically focuses on the decrease in amplitude of a signal over distance or time. Other models may also take into account factors such as interference, diffraction, and multipath propagation, while amplitude decay modeling primarily considers the weakening of the signal itself.