#4: Answer each of the following question for the differential equation (10 pts)
$\frac{d^2c}{dt^2} + 4\frac{dc}{dt} + 7c(t) = 2r(t)$.
a) Draw the state diagram (i.e. signal flow graph (SFG)) including initial conditions.
b) Use Masons gain rule, find the transfer function relating C(s) to R(s). Hint: What do
the initial conditions have to be to obtain the transfer function?
c) Finally find an equation relating C(s) to all the inputs, R(s) and the initial conditions,
using only your SFG.
