function f46(tau)
%Kommentare an pape@molgen.mpg.de

%tau = .001;
v0 = 2;
m = 1;
D = 250000;
n=10000;

omega = (D/m)^.5;

t = 0:tau:(tau*n);

%analytisch
x = v0 ./ omega .* sin(omega.*t);
p = m .* v0 .* cos(omega.*t);

%numerisch
xest = zeros(size(x));
pest = zeros(size(p));
pest(1) = m * v0;

for i=2:length(x),
    xest(i) = xest(i-1) + pest(i-1)/m * tau;
    pest(i) = pest(i-1) - D * xest(i-1) * tau;
end %for i

E = .5 / m .* p.^2 + D / 2 .* x.^2;
Eest = .5 / m .* pest.^2 + D / 2 .* xest.^2;

figure;
subplot(3,1,1)
hold on;
plot(t,x,'b')
plot(t,xest,'r')
title('Ort gegen Zeit');
subplot(3,1,2)
hold on;
plot(t,p,'b')
plot(t,pest,'r')
title('Impuls gegen Zeit');
subplot(3,1,3)
hold on;
plot(t,E,'b')
plot(t,Eest,'r')
title('Energie gegen Zeit');