# 2nd order ODE with time dependent parameters

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민석 김 on 25 Nov 2021
Answered: Pratyush Roy on 1 Dec 2021
I wanna solve a ODE question with matlab The question is
θ''(t) + 2θ'(t) + w* sin θ(t) = τ (t) , τ (t) = 5(1 − exp(−5t))
θ(0) = −π/6 and θ'(0) = 0
w = 10 when 0 ≤ t ≤ 5 or 8 otherwise
t = [0 10]
I wrote the code refer to examples in matlab ode45
ft = linspace(0,10,49); % w = f
for ft = 0:5
f = 10;
end
for ft = 5.2083:10 % w change of time range
f = 8;
end
gt = linspace(0,10,49);
g = 5.*(1-exp(-5.*gt)); % g = τ (t)
tspan = [0 10];
y0 = [-pi/6 0];
[t,y] = ode45(@(t,y) myode(t,y,ft,f,gt,g), tspan, y0);
plot(t,y)
function dydt = myode(t,y,ft,f,gt,g)
dydt = zeros(2,1);
dydt(1) = y(2);
dydt(2) = -2.*y(2)- f.*sin(y(1)) + g
f = interp1(ft,f,t); % Interpolate the data set (ft,f) at time t
g = interp1(gt,g,t); % Interpolate the data set (gt,g) at time t\
end
I got errors like this
numbers of left hand side and right hand side properties are different
오류 발생: untitled2>myode (33번 라인)
dydt(2) = -2.*y(2)- f.*sin(y(1)) + g
오류 발생: untitled2>@(t,y)myode(t,y,ft,f,gt,g) (20번 라인)
[t,y] = ode45(@(t,y) myode(t,y,ft,f,gt,g), tspan, y0);
오류 발생: odearguments (90번 라인)
f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.
오류 발생: ode45 (106번 라인)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);
오류 발생: untitled2 (20번 라인)
[t,y] = ode45(@(t,y) myode(t,y,ft,f,gt,g), tspan, y0);

Pratyush Roy on 1 Dec 2021
Hi 민석 김,
While defining the myode function, one can find the interpolated function first and then compute the first and second order derivatives. The following code snippet might be helpful:
ft = linspace(0,10,49); % w = f
f = zeros(1,49);
for idx = 1:49
if ft(idx)<5.2083
f(idx) = 10;
else
f(idx) = 8;
end
end
gt = linspace(0,10,49);
g = 5.*(1-exp(-5.*gt)); % g = τ (t)
tspan = [0 10];
y0 = [-pi/6 0];
[t,y] = ode45(@(t,y) myode(t,y,ft,f,gt,g), tspan, y0);
plot(t,y)
function dydt = myode(t,y,ft,f,gt,g)
dydt = zeros(2,1);
f = interp1(ft,f,t); % Interpolate the data set (ft,f) at time t
g = interp1(gt,g,t); % Interpolate the data set (gt,g) at time t
dydt(1) = y(2);
dydt(2) = -2.*y(2)- f.*sin(y(1)) + g;
end
Hope this helps!

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