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A) For the adjacent figure': a) Develop the exact and linearized equation of motion by either Newton's Method or Lagrange's Method. Note: assume that the tuning mass (m:) is connected to the main mass (M) by a fixed rigid massless rod and the location of the tuning mass (Lm) is measured from point O'. b) Assuming the system is to be used as a pendulum for a grandfather clock, then the desired natural frequency is ½ Hz (ie. increment 1 second each time the pendulum passes vertical). Due to a serious oversight and design error, when first used without the tuning mass (m:), the clock runs fast by 45 seconds/minute (i.e. the clock counts 105 seconds for every 1 minute of real time). The mass (M) of the uncorrected pendulum (without the tuning mass) is 0.25 kg with a 'cg' location (L) of 0.3 m, and the preferred location (Lm) of the tuning mass (m:) is 1.3 m from point O. Find the moment of inertia (Je) of the uncorrected pendulum and the mass (m:) which must be added to correct the clock. (Use Earth standard gravity = 9.80665 m/s) c) If in the future, the clock were taken to Mars (gravity = 3.711 m/s) as part of a colonization expedition, would the clock run fast or slow? By how much? Would it be possible to correct the clock changing only the value of the tuning mass (m:)? If so, what is the new value of the tuning mass (m:)? M,Jcg e) Lm

A) For the adjacent figure': a) Develop the exact and linearized equation of motion by either Newton's Method or Lagrange's Method. Note: assume that the tuning mass (m:) is connected to the main mass (M) by a fixed rigid massless rod and the location of the tuning mass (Lm) is measured from point O'. b) Assuming the system is to be used as a pendulum for a grandfather clock, then the desired natural frequency is ½ Hz (ie. increment 1 second each time the pendulum passes vertical). Due to a serious oversight and design error, when first used without the tuning mass (m:), the clock runs fast by 45 seconds/minute (i.e. the clock counts 105 seconds for every 1 minute of real time). The mass (M) of the uncorrected pendulum (without the tuning mass) is 0.25 kg with a 'cg' location (L) of 0.3 m, and the preferred location (Lm) of the tuning mass (m:) is 1.3 m from point O. Find the moment of inertia (Je) of the uncorrected pendulum and the mass (m:) which must be added to correct the clock. (Use Earth standard gravity = 9.80665 m/s) c) If in the future, the clock were taken to Mars (gravity = 3.711 m/s) as part of a colonization expedition, would the clock run fast or slow? By how much? Would it be possible to correct the clock changing only the value of the tuning mass (m:)? If so, what is the new value of the tuning mass (m:)? M,Jcg e) Lm

Elements Of Electromagnetics
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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mt 8-A) For the adjacent figure: a) Develop the exact and linearized equation of motion by either Newtons Method or Lagrange
S-A) For the adjacent figure": a) Develop the exact and linearized equation of motion by either Newton's Method or Lagrange's Method. Note: assume that the tuning mass (m:) is connected to the main mass (M) by a fixed rigid massless rod and the location of the tuning mass (Lm) is measured from point 'O'. b) Assuming the system is to be used as a pendulum for a grandfather clock, then the desired natural frequency is ½ Hz (i.e. increment 1 second each time the pendulum passes vertical). Due to a serious oversight and design error, when first used without the tuning mass (m:), the clock runs fast by 45 seconds/minute (i.e. the clock counts 105 seconds for every 1 minute of real time). The mass (M) of the uncorrected pendulum (without the tuning mass) is 0.25 kg with a 'cg' location (L) of 0.3 m, and the preferred location (Lm) of the tuning mass (m:) is 1.3 m from point O'. Find the moment of inertia (Jeg) of the uncorrected pendulum and the mass (m:) which must be added to correct the clock. (Use Earth standard gravity = 9.80665 m/s?) c) If in the future, the clock were taken to Mars (gravity = 3.711 m/s) as part of a colonization expedition, would the clock run fast or slow? By how much? Would it be possible to correct the clock changing only the value of the tuning mass (m;)? If so, what is the new value of the tuning mass (m:)? M,Jcg e(t) Lm
Transcribed Image Text:S-A) For the adjacent figure": a) Develop the exact and linearized equation of motion by either Newton's Method or Lagrange's Method. Note: assume that the tuning mass (m:) is connected to the main mass (M) by a fixed rigid massless rod and the location of the tuning mass (Lm) is measured from point 'O'. b) Assuming the system is to be used as a pendulum for a grandfather clock, then the desired natural frequency is ½ Hz (i.e. increment 1 second each time the pendulum passes vertical). Due to a serious oversight and design error, when first used without the tuning mass (m:), the clock runs fast by 45 seconds/minute (i.e. the clock counts 105 seconds for every 1 minute of real time). The mass (M) of the uncorrected pendulum (without the tuning mass) is 0.25 kg with a 'cg' location (L) of 0.3 m, and the preferred location (Lm) of the tuning mass (m:) is 1.3 m from point O'. Find the moment of inertia (Jeg) of the uncorrected pendulum and the mass (m:) which must be added to correct the clock. (Use Earth standard gravity = 9.80665 m/s?) c) If in the future, the clock were taken to Mars (gravity = 3.711 m/s) as part of a colonization expedition, would the clock run fast or slow? By how much? Would it be possible to correct the clock changing only the value of the tuning mass (m;)? If so, what is the new value of the tuning mass (m:)? M,Jcg e(t) Lm
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