Explanation Given information: The radius of the disk is r . The mass of the disk is m . The length of the rod AB is L 2 . The length of the rod BC is L 2 . Calculation: Write the expression for mass moment of inertia ( I ¯ ) : I ¯ = 1 2 m r 2 The angle α is equal to angular acceleration L 2 r θ ¨ . Write the expression for tangential acceleration ( a t ) : a t = r α Substitute L 2 r θ ¨ for α . a t = r × L 2 r θ ¨ = L 2 θ ¨ Show the free body diagram equation as in Figure (1). Take moment about D in the system for external forces. ( ∑ M D ) e x t e r n a l = − m g r θ − k L θ r 2 Take moment about D in the system for effective forces. ( ∑ M D ) e f f e c t i v e = I ¯ α + m r a t Substitute 1 2 m r 2 for I ¯ , L 2 r θ ¨ for α , and L 2 θ ¨ for a t . ( ∑ M D ) e f f e c t i v e = ( 1 2 m r 2 × L 2 r θ ¨ ) + m r ( L 2 θ ¨ ) = m r L 4 θ ¨ + m r L 2 θ ¨ Equate the moment about C in the system for external and effective forces. ( ∑ M O ) e x t e r n a l = ( ∑ M O ) e f f e c t i v e − m g r θ − k L θ r 2 = m r L 4 θ ¨ + m L 2 r θ ¨ − m r L 4 θ ¨ − m L 2 r θ ¨ − m g r θ − k L r θ 2 = 0 ( m r L 4 + m r L 2 ) θ ¨ + ( m g r + k L r 2<

12th Edition

ISBN: 9781260663778

Author: BEER

Publisher: MCG

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 19.57P

To determine

The frequency (fn) of the resulting vibration in term of m, L, k, and g.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.2, Problem 19.56P

Chapter 19.2, Problem 19.58P

Students have asked these similar questions

Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful! Please do not copy other's work,i will be very very grateful!!Please do not copy other's work,i will be very very grateful!!

= The frame shown is fitted with three 50 cm diameter frictionless pulleys. A force of F = 630 N is applied to the rope at an angle ◊ 43°. Member ABCD is attached to the wall by a fixed support at A. Find the forces indicated below. Note: The rope is tangent to the pully (D) and not secured at the 3 o'clock position. a b •C *су G E e d BY NC SA 2013 Michael Swanbom Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 81 cm b 50 cm с 59 cm d 155 cm For all answers, take x as positive to the right and positive upward. At point A, the fixed support exerts a force of: A = + ĴN and a reaction couple of: →> ΜΑ Member CG is in Select an answer magnitude У as k N-m. and carries a force of N.

The lower jaw AB [Purple 1] and the upper jaw-handle AD [Yellow 2] exert vertical clamping forces on the object at R. The hand squeezes the upper jaw-handle AD [2] and the lower handle BC [Orane 4] with forces F. (Member CD [Red 3] acts as if it is pinned at D, but, in a real vise-grips, its position is actually adjustable.) The clamping force, R, depends on the geometry and on the squeezing force F applied to the handles. Determine the proportionality between the clamping force, R, and the squeezing force F for the dimensions given. d3 d4 R 1 B d1 2 d2 D... d5 F 4 F Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value d1 65 mm d2 156 mm d3 50 mm 45 d4 d5 113 mm 30 mm R = F

Chapter 19 Solutions

VECTOR MECH. FOR EGR: STATS & DYNAM (LL

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 - Prob. 19.6P 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 - Prob. 19.10P

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 frequency ( f n ) of the resulting vibration in term of m , L , k , and g .

Solution Summary: The author calculates the frequency (f_n) of the resulting vibration in terms of m, L, k, and g.

Concept explainers

Videos

The frequency (fn) of the resulting vibration in term of m, L, k, and g.

Want to see the full answer?

Chapter 19 Solutions