﻿ Damped sine wave

# Damped sine wave

## Introduction

Sine waves describe many oscillating phenomena. Often the peak of each wave decreases or dampens as time goes on.

## Step by step

Create an XY data table. There is one X column, and many Y columns. If you have several experimental conditions, place the first into column A, the second into column B, etc.

After entering data, click Analyze, choose nonlinear regression, choose the panel of equations for sine waves, and choose Damped sine wave.

If you know the Y value is zero at time zero, then constrain PhaseShift to a constant value of zero.

You may need to fuss with the initial values for Phaseshift and Wavelength, as our built-in rules for computing the initial values don't always work very well.

## Model

Y= Amplitude*exp(-K*X)*sin((2*pi*X/Wavelength)+PhaseShift

## Interpret the parameters

Amplitude is the height of top of the waves, in Y units.

Wavelength is the time it takes for a complete cycle, in units of X

Frequency is the number of cycles per time unit. It is calculated as the reciprocal of wavelength, and is expressed in the inverse of the time units of X.

PhaseShift in radians. A phaseshift of 0 sets Y equal to 0 at X=0.

K is the decay constant, in the reciprocal of the time units of the X axis.

HalfLlife is the time it takes for the maximum amplitude to decrease by a factor of 2. It is computed as 0.693/K.