ordinary differential equation

i have an equation d(theta)/dt=((P*L^2)/(E*I))*sin(theta*D/L)

L=55.863; D=15.484; E=200*10^9; I=138; P=440*10^6

The initial theta at 1198 years is 0.010degrees.

i have to find theta from the year 1198 to 1990

can someone please help me.its urgent

Answer 1

[Grzegorz Knor]

Use ode45:

L=55.863; D=15.484; E=200*10^9; I=138; P=440*10^6;
ode45(@(t,theta)((P*L^2)/(E*I))*sin(theta*D/L),[1198 1990],0.01)

[12ar.af]

Thank you very much. i have another question.

Can i do the same thing using inline method?if so can you show me how?

and how do u print these theta values?

and if i wanted to find angles for 200 years beyond 1990, how would i do that?

it would be appreciated if u could help.thanks

[Grzegorz Knor]

Just add two output arguments, and colon in tspan:

[T THETA] = ode45(@(t,theta)((P*L^2)/(E*I))*sin(theta*D/L),[1198:1990],0.01)

[Grzegorz Knor]

I don't recomend you inline function, but solution is as follows:

fun = inline('((440*10^6*55.863^2)/(200*10^9*138))*sin(theta*15.484/55.863)','t','theta');

ode45(fun,[1198 1990],0.01)

[12ar.af]

Thanks again.can you tell me how to find theta after 200years from 1990?how do you calculate this?

[Grzegorz Knor]

Solve your equation from 1198 to 1990+200:

[T Y] = ode45(@(t,theta)((P*L^2)/(E*I))*sin(theta*D/L),[1198 1990+200],0.01);

disp(sprintf('year: %i, theta: %.3d',T(end),Y(end)))

[12ar.af]

Can we make the values into a table or something.like year and theta side by side?

[Grzegorz Knor]

Yes, read one of my comment above.

[T THETA] = ode45(@(t,theta)((P*L^2)/(E*I))*sin(theta*D/L),[1198:1990],0.01);

disp([T THETA])