Question

1. The machine to the right includes a rotor of radius e which rotates with frequency $\omega_f$ = 30 rad/s counterclockwise about an axis through point O. The machine has mass 2495 kg and is mounted on a stiff support with k = 1x$10^6$ N/m and c = 3000 Ns/m. An engineer (who didn't take Mechanical Vibrations) unsuspectingly attaches a sensor to the edge of the rotor (at a length e from point O). The sensor has mass m = 5 kg. He notices that when the machine is running at operating speed, it has a vertical vibration of 0.0025 m. The equation of motion for this system is given as: $M\ddot{x} + c\dot{x} + kx = me\omega_f^2 sin(\omega_f t)$ a. Show that the unbalance mass is located 0.7 m from point O. b. Find the steady-state position of the unbalance mass at 0.5 s. c. What is the maximum force exerted to the base?

          1. The machine to the right includes a rotor of radius e which rotates with
frequency $\omega_f$ = 30 rad/s counterclockwise about an axis through point O. The
machine has mass 2495 kg and is mounted on a stiff support with k = 1x$10^6$
N/m and c = 3000 Ns/m.

An engineer (who didn't take Mechanical Vibrations) unsuspectingly attaches
a sensor to the edge of the rotor (at a length e from point O). The sensor has
mass m = 5 kg. He notices that when the machine is running at operating
speed, it has a vertical vibration of 0.0025 m.

The equation of motion for this system is given as:
$M\ddot{x} + c\dot{x} + kx = me\omega_f^2 sin(\omega_f t)$

a. Show that the unbalance mass is located 0.7 m from point O.

b. Find the steady-state position of the unbalance mass at 0.5 s.

c. What is the maximum force exerted to the base?

1 the machine to the right includes a rotor of radius e which rotates with frequency omegaf 30 rads counterclockwise about an axis through point o the machine has mass 2495 kg and is mounte 12116

Added by Robert G.

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