Question

Problem 4: The unbalanced rotor shown in the figure is pinned to a frame and supported by a spring and damper. If the total mass is m while the mass center G is located at an eccentricity of $epsilon$ from the center of rotation C, a) find the damped natural frequency; b) what is the steady-state amplitude of vibration when the rotor spins at an angular speed of $omega = 8pi$ rad with: $k = 32$ N/m, $b = 16$ N/(m/s), $m = 4$ kg, $epsilon = 2.5$ cm c) If the system is undamped (i.e., $b = 0$ N/(m/s)) for what range of operating speeds ($omega$) will the amplitude of the force transmitted to the ground $F_T$ be less than 1N.

          Problem 4:
The unbalanced rotor shown in the figure is
pinned to a frame and supported by a spring
and damper. If the total mass is m while the
mass center G is located at an eccentricity of
$epsilon$ from the center of rotation C,
a) find the damped natural frequency;
b) what is the steady-state amplitude of
vibration when the rotor spins at an angular
speed of $omega = 8pi$ rad with:
$k = 32$ N/m, $b = 16$ N/(m/s),
$m = 4$ kg, $epsilon = 2.5$ cm
c) If the system is undamped (i.e., $b = 0$ N/(m/s)) for what range of operating speeds ($omega$) will the amplitude of the force transmitted to the ground $F_T$ be less than 1N.

Problem 4:
The unbalanced rotor shown in the figure is
pinned to a frame and supported by a spring
and damper. If the total mass is m while the
mass center G is located at an eccentricity of
epsilon from the center of rotation C,
a) find the damped natural frequency;
b) what is the steady-state amplitude of
vibration when the rotor spins at an angular
speed of omega = 8pi rad with:
k = 32 N/m, b = 16 N/(m/s),
m = 4 kg, epsilon = 2.5 cm
c) If the system is undamped (i.e., b = 0 N/(m/s)) for what range of operating speeds (omega) will the amplitude of the force transmitted to the ground FT be less than 1N.

Added by Sean W.

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