Question

4. (a) The figure on the right shows a dynamic vibration absorber, which has been modeled as a cantilever beam with a motor attached. The spring $k_2$ and mass $m_2$ attached act as the vibration absorber. The cantilever beam and motor have been approximated as a spring $k$ and a mass $m$. The displacements $x$ and $x_2$ are measured from the static equilibrium positions when $f = 0$. Derive the transfer functions for $\frac{x}{f}$ and $\frac{x_2}{f}$ for this system. [10] (b) Draw the nested integral simulation diagram for this system (with $x$ as the output). [5] (c) Write the state-space equations of the system using the simulation diagram. [5]

          4. (a) The figure on the right shows a dynamic
vibration absorber, which has been modeled as a
cantilever beam with a motor attached. The
spring $k_2$ and mass $m_2$ attached act as the
vibration absorber. The cantilever beam and
motor have been approximated as a spring $k$ and
a mass $m$. The displacements $x$ and $x_2$ are
measured from the static equilibrium positions
when $f = 0$.
Derive the transfer functions for $\frac{x}{f}$ and $\frac{x_2}{f}$ for
this system.
[10]
(b) Draw the nested integral simulation diagram for this system (with $x$ as the output). [5]
(c) Write the state-space equations of the system using the simulation diagram. [5]

4. (a) The figure on the right shows a dynamic
vibration absorber, which has been modeled as a
cantilever beam with a motor attached. The
spring k2 and mass m2 attached act as the
vibration absorber. The cantilever beam and
motor have been approximated as a spring k and
a mass m. The displacements x and x2 are
measured from the static equilibrium positions
when f = 0.
Derive the transfer functions for (x)/(f) and (x2)/(f) for
this system.
[10]
(b) Draw the nested integral simulation diagram for this system (with x as the output). [5]
(c) Write the state-space equations of the system using the simulation diagram. [5]

Added by Jose Miguel C.

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