Explanation Given information: The period of oscillation = 2 τ 0 The forces corresponding to the disc are shown in the free body diagram below: α = θ ¨ a t = r α = r θ ¨ And moment of inertia is I = m r 2 2 Now taking moment about point C, ∑ M C = ( ∑ M C ) e f f w r sin ( β − θ ) − w r sin ( β + θ ) = 2 w g r a t + I α w r [ sin ( β − θ ) − sin ( β + θ ) ] = − 2 w r sin θ cos β ( 2 w r 2 g + W r 2 2 g ) θ ¨ + ( 2 w r cos β ) θ = 0 Since, sin θ ≈ θ Compare the above equation with un-damped equation of vibration;

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

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Gen…

Videos

Question

Chapter 19.2, Problem 19.44P

To determine

The angle β for a given period of oscillation.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.2, Problem 19.43P

Chapter 19.2, Problem 19.45P

Students have asked these similar questions

Student Name: Student Id: College of Applied Engineering Al-Muzahmiyah Branch Statics (AGE 1330) Section-1483 Quiz-2 Time: 20 minutes Date: 16/02/2025 Q.1. A swinging door that weighs w=400.0N is supported by hinges A and B so that the door can swing about a vertical' axis passing through the hinges (as shown in below figure). The door has a width of b=1.00m and the door slab has a uniform mass density. The hinges are placed symmetrically at the door's edge in such a way that the door's weight is evenly distributed between them. The hinges are separated by distance a=2.00m. Find the forces on the hinges when the door rests half-open. Draw Free body diagram also. [5 marks] [CLO 1.2] Mool b ర a 2.0 m B 1.0 m

For the walking-beam mechanism shown in Figure 3, find and plot the x and y coordinates of the position of the coupler point P for one complete revolution of the crank O2A. Use the coordinate system shown in Figure 3. Hint: Calculate them first with respect to the ground link 0204 and then transform them into the global XY coordinate system. y -1.75 Ꮎ Ꮎ 4 = 2.33 0242.22 L4 x AP = 3.06 L2 = 1.0 W2 31° B 03 L3 = 2.06 P 1 8 5 .06 6 7 P'

The link lengths, gear ratio (2), phase angle (Ø), and the value of 02 for some geared five bar linkages are defined in Table 2. The linkage configuration and terminology are shown in Figure 2. For the rows assigned, find all possible solutions for angles 03 and 04 by the vector loop method. Show your work in details: vector loop, vector equations, solution procedure. Table 2 Row Link 1 Link 2 Link 3 Link 4 Link 5 λ Φ Ө a 6 1 7 9 4 2 30° 60° P y 4 YA B b R4 R3 YA A Gear ratio: a 02 d 05 r5 R5 R2 Phase angle: = 0₂-202 R1 05 02 r2 Figure 2. 04 X

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 angle β for a given period of oscillation.

Solution Summary: The author explains the angle beta for a given period of oscillation.

Concept explainers

Videos

The angle β for a given period of oscillation.

Want to see the full answer?

Chapter 19 Solutions