Question

A machine part is modeled as a pendulum connected to a spring and damper as illustrated. The mass of the pendulum rod is $m_r = 2$ kg and the mass at the pendulum tip is $m = 8$ kg, the spring stiffness is k=250 N/m, and the damping coefficient is c = 7 N.s/m. The length of the rod is L = 1 m and length $l = 0.5$ m. Note: The weights of both the tip mass and the rod mass are included in the equation of motion. [2 Mark] The natural frequency $\omega_n$, rad/s, of the system is. (hint: derive the equation of motion and linearize it.) $\circ$ 4.68576 $\circ$ 2.6865 $\circ$ 9.37152 $\circ$ 6.24768 [2 Mark] The damping ratio $\zeta$ $\circ$ 0.0195534 $\circ$ 0.0227853 $\circ$ 0.0161598 $\circ$ 0.0274717 [1 Mark] is this stable system? $\circ$ Yes $\circ$ No

          A machine part is modeled as a pendulum connected to a spring and damper as illustrated. The mass of the pendulum rod is $m_r = 2$ kg and the mass at the pendulum tip is $m = 8$ kg, the spring stiffness is
k=250 N/m, and the damping coefficient is c = 7 N.s/m. The length of the rod is L = 1 m and length $l = 0.5$ m.
Note: The weights of both the tip mass and the rod mass are included in the equation of motion.
[2 Mark] The natural frequency $\omega_n$, rad/s, of the system is. (hint: derive the equation of motion and linearize it.)
$\circ$ 4.68576
$\circ$ 2.6865
$\circ$ 9.37152
$\circ$ 6.24768
[2 Mark] The damping ratio $\zeta$
$\circ$ 0.0195534
$\circ$ 0.0227853
$\circ$ 0.0161598
$\circ$ 0.0274717
[1 Mark] is this stable system?
$\circ$ Yes
$\circ$ No

A machine part is modeled as a pendulum connected to a spring and damper as illustrated. The mass of the pendulum rod is mr = 2 kg and the mass at the pendulum tip is m = 8 kg, the spring stiffness is
k=250 N/m, and the damping coefficient is c = 7 N.s/m. The length of the rod is L = 1 m and length l = 0.5 m.
Note: The weights of both the tip mass and the rod mass are included in the equation of motion.
[2 Mark] The natural frequency , rad/s, of the system is. (hint: derive the equation of motion and linearize it.)
∘ 4.68576
∘ 2.6865
∘ 9.37152
∘ 6.24768
[2 Mark] The damping ratio ζ
∘ 0.0195534
∘ 0.0227853
∘ 0.0161598
∘ 0.0274717
[1 Mark] is this stable system?
∘ Yes
∘ No

Added by Nancy F.

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