Hi Aleem Andrew,
I believe you are trying to implement t-4x(t)=x’’(t) in Simulink.
Your model seems to be correct, and the Simulink engine is trying to solve the equation with default initial conditions as x(0)=0 and x’(0)=0. The output for x(t) for the above differential equation seems to be as below,
This is the curve for the equation x(t)=t/4-sin(2*t)/8. This can be further verified by using “dsolve” for solving the above said equation.
syms x(t) a b
eqn = diff(x,t,2) == t-4*x;
Dx = diff(x,t);
cond = [x(0)==0, Dx(0)==0];% initial condition x(0)=0 and x’(0)=0
xSol(t) = dsolve(eqn,cond);
t=1:0.2:10;
plot(xSol(t))
The solution x(t)= t/4 + C1*cos(2*t) - C2*sin(2*t) is when initial conditions are not present for the differential equation. That’s why the plot seems different as it’s for x(t)=t/4-sin(2*t)/8. I hope this helps resolve your query.
Here is the link for additional documentation:
Thanks and regards,
Tushar Behera
