4. The maximum vertical force applied to the machine by the unbalanced mass (in Newtons) if the motor is spinning at Win,1 = 500 RPM. 5. The percent reduction in vibration transmitted to the foundation if the motor is spinning at Win,1 = 500 RPM. (Note: the percentage is the transmission ratio (TR) multiplied by 100.) 1 Problem Consider the following scale prototype of a measurement unit operating in the presence of vi- brations from an unbalanced motor. Dynamic vibration absorber Measuring point at measuring probe position Unbalance motor Figure 1: Left: A dynamic vibration absorber (DVA) mounted above the unit. Right: A vibration isolator base that the unit rests on. Image source: [1]. Before adding the DVA (shown above) the original system (machine and isolator mounts) were modeled using a lumped-parameter model (sketched below). The model approximated this sys- tem as a rotating machine of total mass M = 50 kg with a unbalanced mass m = 0.08 kg at a distance r = 0.05 m from the center of a spinning motor shaft that is mounted on a vibration isolator with stiffness k = 50,000 N/m and damping b = 0.8 N-s/m. For this system, determine: k W r m нич 1. The natural frequency in rotations per minute (RPM). 2. The resonant frequency in rotations per minute (RPM). 3. The phase shift at resonance in degrees. M

4. The maximum vertical force applied to the machine by the unbalanced mass (in Newtons) if the motor is spinning at Win,1 = 500 RPM. 5. The percent reduction in vibration transmitted to the foundation if the motor is spinning at Win,1 = 500 RPM. (Note: the percentage is the transmission ratio (TR) multiplied by 100.) 1 Problem Consider the following scale prototype of a measurement unit operating in the presence of vi- brations from an unbalanced motor. Dynamic vibration absorber Measuring point at measuring probe position Unbalance motor Figure 1: Left: A dynamic vibration absorber (DVA) mounted above the unit. Right: A vibration isolator base that the unit rests on. Image source: [1]. Before adding the DVA (shown above) the original system (machine and isolator mounts) were modeled using a lumped-parameter model (sketched below). The model approximated this sys- tem as a rotating machine of total mass M = 50 kg with a unbalanced mass m = 0.08 kg at a distance r = 0.05 m from the center of a spinning motor shaft that is mounted on a vibration isolator with stiffness k = 50,000 N/m and damping b = 0.8 N-s/m. For this system, determine: k W r m нич 1. The natural frequency in rotations per minute (RPM). 2. The resonant frequency in rotations per minute (RPM). 3. The phase shift at resonance in degrees. M

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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