Laplace transform of a massspringdamper system
3,057
Apply the Laplace transform to both equations, term by term (since the Laplace transform is a linear operator). Then you will have two equations in terms of $X (s) $ and $U (s) $. Combine the equations to eliminate $U (s) $. Then perform the algebra to isolate $X (s)$ on one side of the equation.
Related videos on Youtube
Author by
James
Updated on December 02, 2020Comments

James almost 3 years
We consider integral control of a massspringdamper system, that is a coupled system
$$\ddot x(t) + 5\dot x(t) + 4x(t) = u(t),$$ $$\dot u(t) = k(r  x(t))$$ where k is a positive parameter and r is a desired set point.
Verify that if the initial conditions are zero $($i.e. $x(0) = 0$, $\dot x(0) = 0 $ and $u(0) = 0$$)$, then, $$X(s) = \frac{k}{s(s^2+5s+4)+k}\cdot \frac{r}{s}$$ How do I go about reaching this solution?