Consider the following spring-mass-damper system with input u(t).
M
z
k
b
k
b
u
The input (independent variable) to this system is the displacement u. The equations for this suspension system are
10$\ddot{z}$ + $f_1$ + $f_2$ = 0
$f_1$ = 100(z - v)
$f_2$ = 5($\dot{z}$ - $\dot{v}$)
$f_3$ = 100(v - u)
$f_4$ = 5($\dot{v}$ - $\dot{u}$)
$f_1$ + $f_2$ - $f_3$ - $f_4$ = 0
(a) List the unknowns (dependent variables) and confirm that the number of equations matches the number of
unknowns.
(b) Use the "D" operator to convert the differential equations to algebraic equations.
(c) Eliminate $f_1$, then eliminate $f_2$, then eliminate $f_3$, and then eliminate $f_4$. How many equations with which unknowns
do you have left?
(d) Use MATLAB to solve the system of equations for the variable z, by creating an m-file.
