Question

F(t) k F(t) m m b (i) b b m k w F(t) m (ii) b 6. Consider the mechanical systems shown above. The system parameters are the same for both systems, and both systems are driven by a single input. (a) Obtain the state equations of both systems if $x_1$ and $x_2$ are the velocities of both masses, and $x_3$ is the force on the spring. (b) Determine if the systems are controllable or not. (c) If the mass values were different, e.g., $m_1$ and $m_2$, would the systems be controllable?

          F(t)
k
F(t)
m
m
b
(i)
b
b
m
k
w
F(t)
m
(ii)
b
6. Consider the mechanical systems shown above. The system parameters are the same for both
systems, and both systems are driven by a single input.
(a) Obtain the state equations of both systems if $x_1$ and $x_2$ are the velocities of both masses, and
$x_3$ is the force on the spring.
(b) Determine if the systems are controllable or not.
(c) If the mass values were different, e.g., $m_1$ and $m_2$, would the systems be controllable?

F(t)
k
F(t)
m
m
b
(i)
b
b
m
k
w
F(t)
m
(ii)
b
6. Consider the mechanical systems shown above. The system parameters are the same for both
systems, and both systems are driven by a single input.
(a) Obtain the state equations of both systems if x1 and x2 are the velocities of both masses, and
x3 is the force on the spring.
(b) Determine if the systems are controllable or not.
(c) If the mass values were different, e.g., m1 and m2, would the systems be controllable?

Added by Richard P.

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