Question

Matlab:

Study the effects of damping by starting a pendulum (use l = 9.81 m and q = 0.1) with an initial displacement (θ = 0.5 rad, for example). Estimate the time constant for the decay of the pendulum oscillation obtained with these values.

Answer 1

% compute the knee angle (térdszög számolása)
v1 = m1(:,2:3)-m2(:,2:3);
v2 = m3(:,2:3)-m2(:,2:3);
% magnitude of both vectors (mindkét vektor hossza)
magv1 = sqrt(v1(:,1).^2 + v1(:,2).^2);
magv2 = sqrt(v2(:,1).^2 + v2(:,2).^2);
% scalar product of v1 and v2 (v1 és v2 skalárszorzata)
v1dotv2 = dot(v1,v2,2);
% computing the angle (szögek számítása)
alpharad = acos(v1dotv2./(magv1.*magv2));
% plot the results (Eredmény kiiratása)
offset = 119; % offset
Tsamp = 1/30; % sampling time - idő mintavétel
t = (0:length(alpharad)-1)'*Tsamp; % time vector
alpha=alpharad*180/pi-offset;
figure(1)
subplot(1,2,1)
plot(m1(:,3),-m1(:,2),'rx', m2(:,3),-m2(:,2),'gx', m3(:,3),-m3(:,2),'bx')
grid
xlabel('x koordinata [pixel]')
ylabel('y koordinata [pixel]')
subplot(1,2,2)
plot(t, alpha)
grid
xlabel('ido [s]' )
ylabel('térdszög [fok]')