Explanation Given information: Distance G A = K ¯ 2 r ¯ For equation of motion taking moment about point O, ∑ M 0 = ∑ ( M 0 ) e f f − W r ¯ sin θ = I ¯ α + m a ¯ t r ¯ − m g r ¯ sin θ = m k ¯ 2 θ ¨ + m r ¯ 2 θ ¨ m k ¯ 2 θ ¨ + m r ¯ 2 θ ¨ + m g r ¯ sin θ = 0 m ( k ¯ 2 + r ¯ 2 ) θ ¨ + m ( g r ¯ sin θ ) = 0 ( k ¯ 2 + r ¯ 2 ) θ ¨ + ( g r ¯ sin θ ) = 0 θ ¨ + g r ¯ k ¯ 2 + r ¯ 2 sin θ = 0 _ _ _ _ _ _ ( 1 ) Here, W = m g α = θ ¨

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

See similar textbooks

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Videos

Question

Chapter 19.2, Problem 19.53P

To determine

The smallest period of oscillation at a distance r from point O is equal to k¯.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.2, Problem 19.52P

Chapter 19.2, Problem 19.54P

Students have asked these similar questions

%94 KB/S Find : 1. dynamic load on each bearing due to the out-of-balance couple; and 2. kinetic energy of the complete assembly. [Ans. 6.12 kg: 8.7 N-m] L 2. 3. 4. 5. 1. 2. 5. DO YOU KNOW? Why is balancing of rotating parts necessary for high speed engines? Explain clearly the terms "static balancing' and 'dynamic balancing'. State the necessary conditions to achieve them. Discuss how a single revolving mass is balanced by two masses revolving in different planes. Chapter 21: Balancing of Rotating Masses .857 Explain the method of balancing of different masses revolving in the same plane. How the different masses rotating in different planes are balanced? OBJECTIVE TYPE QUESTIONS The balancing of rotating and reciprocating parts of an engine is necessary when it runs at (a) slow speed (b) medium speed (c) high speed A disturbing mass, attached to a rotating shaft may be balanced by a single mass m, attached in the same plane of rotation as that of my such that (a) (b) F For static…

Provide a real-world usage example of the following: Straightness Circularity Parallelism What specific tools, jigs, and other devices are used to control the examples you provided?

856 Theory of Machines 5. A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and 80 kg respectively. The angle between A and C is 90° and that between C and D is 135° Determine the magnitude of the masses in planes B and E and their positions to put the shaft in complete rotating balance. [Ans. 12 kg, 15 kg; 130° and 24° from mass A in anticlockwise direction]

Chapter 19 Solutions

Vector Mechanics For Engineers

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - A 20-lb block is initially held so that the...Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - A 5-kg fragile glass vase is surrounded by packing...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The smallest period of oscillation at a distance r from point O is equal to k ¯ .

Solution Summary: The author explains that the smallest period of oscillation at a distance r from point O is equal to stackrel k.

Concept explainers

Videos

The smallest period of oscillation at a distance r from point O is equal to k¯.

Want to see the full answer?

Chapter 19 Solutions