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houlahound
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I collected data on a periodic mechanical motion. The amplitude is damped linearly. What mathematical function models linear amplitude decay. All I can find is exponential decay of a sine wave.
A Linear Amplitude Decay Function is a mathematical function that describes the gradual decrease in amplitude or strength of a signal over time. It is commonly used to model the attenuation of sound or light waves as they travel through a medium.
A Linear Amplitude Decay Function can be represented by the equation y = ae-bx, where a is the initial amplitude, b is the decay constant, and x is the distance or time traveled.
The rate of amplitude decay in a linear function is primarily affected by the distance or time traveled, as well as the properties of the medium through which the signal is traveling. Other factors such as temperature and pressure can also play a role.
A Linear Amplitude Decay Function decreases at a constant rate, while an Exponential Decay Function decreases at an increasing rate. In other words, the slope of a Linear Amplitude Decay Function is constant, while the slope of an Exponential Decay Function becomes steeper over time.
Linear Amplitude Decay Functions are commonly used in fields such as acoustics, optics, and electronics to model the decrease in signal strength over distance or time. They are also used in financial analysis to model the depreciation of assets over time.