how should I add to cord

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정연
정연 2023 年 12 月 2 日
回答済み: Sulaymon Eshkabilov 2023 年 12 月 2 日
syms c m k w w_n c_c zeta x X p;
w_n = sqrt(k/m); % natural frequency of undamped oscillation
c_c = 2*m*w_n; % critical damping
zeta = c/ c_c; % damping factor
p = atan(c*w/(k-m*w^2)); % Φ
X = F_0/(2*zeta*k); % amplitude of oscillation
% the differential equation and its complete solution
% including the transient term
% x" + 2*zeta*x' + (w_n)^2*x = F_0*sin(wt)/m
eqn = F_0/k - sin(w*t - p)/sqrt((1-(w/w_n)^2)+(2*zeta*w/w_n)^2)...
+ X*exp(-zeta*w_n*t)*sin(sqrt(1-zeta^2)*w_n*t+p);
% Solve the differential equation
sol = dsolve(eqn);
% Display the solution
disp('Solution:');
disp(sol);
% Plot the solution
figure;
plot(sol, [0, 10], 'LineWidth', 2);
title('Solution of the Mass-Damper-Spring System with Harmonic Excitation');
xlabel('Time');
ylabel('Displacement');
I've written the code up to this point. I need to draw the attached picture. How should I use the plot?
  1 件のコメント
Dyuman Joshi
Dyuman Joshi 2023 年 12 月 2 日
There are undefined parameters in your code.
You are using dsolve, but have not defined a differential equation. And I don't see a relation between the differential equation in the comments and the equation defined in the code just below.

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回答 (1 件)

Sulaymon Eshkabilov
Sulaymon Eshkabilov 2023 年 12 月 2 日
How you are trying to solve your given exercise is not correct.
Here is one function that I wrote to simulate the 1 DOF spring-mass-damper system that is what you're trying to plot.
M=2; S=50;
omegaN=sqrt(S/M);
omega=0:.2:10;
r=omega./omegaN;
zeta=0:0.2:1;
zeta_1DOF_SMD(M, zeta, S, omega)
function zeta_1DOF_SMD(M, zeta, S, omega)
% HELP. Study damping ratio (zeta) influence on Amplitude change
% M - Mass of the system
% D - Damping coefficient of the system ranges (row matrix): 0...
% S - Stiffness of the system
%{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Written by Sulaymon L. ESHKABILOV, PhD %
% April, 2013 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%}
close all
if nargin<1
M=2.5; S=25; omegaN=sqrt(S/M); omega=0:.2:10; r=omega./omegaN; zeta=0:0.2:1;
end
omegaN=sqrt(S/M);
r=omega/omegaN;
Mag=zeros(length(zeta), length(r));
Theta=ones(length(zeta), length(r));
for ii=1:length(zeta)
for k=1:length(r)
Mag(ii,k)=1/sqrt((1-r(k)^2)^2+(2*zeta(ii)*r(k))^2);
Theta(ii,k)=atan2(2*zeta(ii)*r(k), (1-r(k)^2));
end
end
%
close all
Labelit = {};
Colorit = 'bgrmkgbckmbgrygr';
Lineit = '--:-:--:-:--:----:----:--';
Markit = 'oxs+*^v<p>.xsh+od+*^v';
for m=1:length(zeta)
Stylo = [Colorit(m) Lineit(m) Markit(m)];
Labelit{m} = ['\zeta= ' num2str(zeta(m))];
semilogy(r, Mag(m,:), Stylo, 'linewidth', 1.5), hold on
end
legend(Labelit{:})
title('\zeta influence on Response Amplitude change'),
xlabel('r = \omega/\omega_n'), ylabel('Normalized Amplitude'), axis tight; grid on; ylim([0, 5])
hold off
figure
for m=1:length(zeta)
Stylo = [Colorit(m) Lineit(m) Markit(m)];
Labelit{m} = ['\zeta= ' num2str(zeta(m))];
plot(r, Theta(m,:), Stylo, 'linewidth', 1.5)
hold on
end
legend(Labelit{:}), axis tight, grid on, xlim([0, 2]),
title('\zeta influence on Phase change')
xlabel('r = \omega/\omega_n '), ylabel('Phase, \theta(r)')
end

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