All transfer functions are to be in standard form: (1) descending powers of s in the
numerator and denominator, (2) grouping the coefficients in front of s terms, and (3) should
contain no fractions. You must draw all relevant FBDs you use to derive EOMs
Question 4:
4. (12) Consider the mechanical system shown below. Assume that $u(t)$ is the force
applied to the cart and the input into the system. The displacement $x(t)$ is measured
from the equilibrium position and is the output of the system. Obtain, algebraically,
the transfer function, $X(s)/U(s)$, of the system using the given coordinate references.
x (Output)
k1
k2
www
m
u(t)
(Input force)
Show all the steps in your derivation. Notate if you use Mathematica to simplify your
algebra from one step to the next.
