Please help me solve this differential equation
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please i will like to solve this eqution for w=188 rad/s
Please take a2=3 a3=2, b2=5 and b3=2
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John D'Errico
2022년 7월 18일
You tell us what the value of w is, but not all of the other important parameters. They are just as important. Thus what are a2, a3, b2 b3? If you don't have them, then no numerical solution will be possible. My expectation is no analytical solution will exist in any case, so a numerical solution is your only option.
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Sam Chak
2022년 7월 19일
Hi @Armel Kapso
Some basic code from the ode45 documentation. Probably looks like this, try manupulating the parameters yourself.
tspan = [0 1]; % simulation time interval
initv = [1 0]; % initial values
[t, x] = ode45(@odefcn, tspan, initv);
plot(t, x(:, 1), 'linewidth', 1.5)
grid on
xlabel({'$t$'}, 'Interpreter', 'latex')
ylabel({'$x(t)$'}, 'Interpreter', 'latex')
title('System Response')
function dxdt = odefcn(t, x)
dxdt = zeros(2, 1);
a2 = 3;
a3 = 2;
b2 = 5;
b3 = 2;
omega = 188;
num = 2*a3*omega^3*sin(x(1) - omega*t)*x(2) + 2*a3*omega*sin(x(1) - omega*t)*x(2)^3 - b3*sin(x(1)) - b3*sin(omega*t);
den = 2*a2 - 2*a3*omega*(2*x(2) + omega)*cos(x(1) - omega*t);
dxdt(1) = x(2);
dxdt(2) = num/den;
end
댓글 수: 9
Torsten
2022년 7월 29일
Corrected.
a2 = 3;
a3 = 2;
b2 = 5;
b3 = 2;
omega = 210;
f = @(t,x) [x(2);(2*a3*omega^3*sin(x(1)-omega*t)*x(2)+...
2*a3*omega*sin(x(1)-omega*t)*x(2)^3-...
b3*sin(x(1))-b3*sin(omega*t))/(2*a2-2*a3*omega*(2*x(2)+omega)*cos(x(1)-omega*t))];
tspan = linspace(0, 88, 8801);
init = [1 1];
options = odeset('RelTol',1e-8,'AbsTol',1e-8);
[t, x] = ode15s(f, tspan, init, options);
plot(x(:,1), x(:,2))
추가 답변 (1개)
Chunru
2022년 7월 19일
편집: Chunru
2022년 7월 19일
opts = odeset('RelTol', 1e-2, 'AbsTol', 1e-4);
[t, x] = ode45(@diffeqn, [0 1], [0.1; .1], opts);
whos
plot(t, x(:,2))
function dxdt = diffeqn(t, x)
a2=3; a3=2; b2=5; b3=2; w=188;
% Check this out
dxdt(1, 1) = x(2);
dxdt(2, 1) = ( (2*a3*w^3*sin(x(2)-w*t))*x(1) + ...
(2*a3*w*sin(x(2)-w*t))*x(1).^3 + ...
(-b2*sin(w*t) - b3*sin(x(2))) ) ./ ...
( 2*a2 -2*a3*w*(2*x(1)+w)*cos(x(2)-w*t) );
end
댓글 수: 6
Chunru
2022년 7월 19일
You need to save the code in a file, e.g., testdiff.m. Then run the program testdiff.m
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