From DDL Wiki

Contents 1 Code 1.1 Logarithmic Decrement 1.1.1 readenct.m 1.1.2 num4.m

Code

Logarithmic Decrement

readenct.m

Reads in the text file generated by the MSE Rectilinear apparatus.

function [t,f,val]=readenct(filename,vd,encnum)

a=textread(filename,'','headerlines',23);
if strcmp(vd,'d') 
    val=-a(:,encnum+1);
end
if strcmp(vd,'v') 
    val=-a(:,encnum+5);
end
t=a(:,1);
f=a(:,2);

num4.m

Using the data returned by readenct, allows determination of physical constants using logarithmic decrament analysis.

[time,force,displacement]=readenct('medium_natural.txt','d',1);
figure(1)
plot(time,displacement+0.1198);
axis([10.6 11.4 -4 4.2])


a=ginput
c=max(a)

figure(2)
plot(time,displacement+0.1198);
axis([10.6 11.4 -4 4.2])


b=ginput
d=max(b)

prompt={'Number of Peaks in between','X Coordinate First MAX.','X Coordinate Second MAX.'}
name='Get User Input';
numlines=1;
defaultanswer={'0','0','0'};
answer=inputdlg(prompt,name,numlines,defaultanswer);
n=str2double(answer{1});
x1=str2double(answer{2});
x2=str2double(answer{3});

T=(x2-x1)/(n);
dampingRatio=((1/(n-1))*(log(c(1,2)/d(1,2))))/sqrt((4*pi^2)+((1/(n-1))*(log(c(1,2)/d(1,2))))^2)
naturalFrequency=((1/(n-1))*log(c(1,2)/d(1,2)))/(dampingRatio*T)
dampedNaturalFrequency=naturalFrequency*sqrt(1-dampingRatio^2)
m=0.79;
k=naturalFrequency^2*m
CoefficientOfDamping=dampingRatio*2*sqrt(k*m)