Solving differential equations with Simulink

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Can someone explain what differential equation is being solved below? The input is a ramp input.

Accepted Answer

Birdman
Birdman on 27 Jan 2021
If you consider the ramp imput as a function
r(t)=t;
then the equation becomes
If you code this in MATLAB:
syms x(t)
eq=t-4*x==diff(x,2);
X(t)=dsolve(eq);%without giving initial conditions
and you will obtain
X(t) =
t/4+C1*cos(2*t)-C2*sin(2*t)

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