A light shaft supported in bearings at its ends carries a rotor of mass m at its mid span. When displaced laterally, the elastic restoring force due to flexure of the shaft is Kper unit deflection. If the centre of gravity of the beam is at a distance e from the axis of rotation when at rest, (a) show that the elastic deflection y of the shaft at mid span, at an angular velocity of is given by w²e y = {-w²} (b) Explain how the magnitude and direction of y change as oois increased from zero to higher values. (c) If e 0.25 mm and the whirling speed is 1000 rev/min, find the speed range over which the magnitude of y will exceed 1.30 mm.
A light shaft supported in bearings at its ends carries a rotor of mass m at its mid span. When displaced laterally, the elastic restoring force due to flexure of the shaft is Kper unit deflection. If the centre of gravity of the beam is at a distance e from the axis of rotation when at rest, (a) show that the elastic deflection y of the shaft at mid span, at an angular velocity of is given by w²e y = {-w²} (b) Explain how the magnitude and direction of y change as oois increased from zero to higher values. (c) If e 0.25 mm and the whirling speed is 1000 rev/min, find the speed range over which the magnitude of y will exceed 1.30 mm.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![A light shaft supported in bearings at its ends carries a rotor of mass m at its mid span. When
displaced laterally, the elastic restoring force due to flexure of the shaft is Kper unit deflection. If
the centre of gravity of the beam is at a distance e from the axis of rotation when at rest,
(a)
show that the elastic deflection y of the shaft at mid span, at an angular velocity of wis
given by
w²e
y =
(b)
Explain how the magnitude and direction of y change as oois increased from zero to higher
values.
(c)
If e = 0.25 mm and the whirling speed is 1000 rev/min, find the speed range over which
the magnitude of y will exceed 1.30 mm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1770a0c6-60a2-4197-ba3a-e76b7f379658%2F510c70e4-10ce-428c-9e70-0bd4c49d61e7%2Fipzue4g_processed.png&w=3840&q=75)
Transcribed Image Text:A light shaft supported in bearings at its ends carries a rotor of mass m at its mid span. When
displaced laterally, the elastic restoring force due to flexure of the shaft is Kper unit deflection. If
the centre of gravity of the beam is at a distance e from the axis of rotation when at rest,
(a)
show that the elastic deflection y of the shaft at mid span, at an angular velocity of wis
given by
w²e
y =
(b)
Explain how the magnitude and direction of y change as oois increased from zero to higher
values.
(c)
If e = 0.25 mm and the whirling speed is 1000 rev/min, find the speed range over which
the magnitude of y will exceed 1.30 mm.
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