VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
12th Edition
ISBN: 9781260265521
Author: BEER
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 19.3, Problem 19.89P
To determine
(a)
The frequency of oscillations.
To determine
(b)
The smallest value of ‘ a’ for oscillations occur.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Two identical circular cylinders of radius r and mass m each, are connected by a
spring, as shown below. Derive the equations of motion using Lagrange's equations. Please
indicate the lowest natural vibration frequency. (1 =mr?)
k
m
An inverted pendulum consisting of a rigid bar ABC of length l and mass m is supported by a pin and bracket at C. A spring of constant k is attached to the bar at B and is undeformed when the bar is in the vertical position shown. Determine (a ) the frequency of small oscillations, (b ) the smallest value of a for which these oscillations will occur.
An 800-g rod AB is bolted to a 1.2-kg disk. A spring of constant k = 12 N/m is attached to the center of the disk at A and to the wall at C . Knowing that the disk rolls without sliding, determine the period of small oscillations of the system.
Chapter 19 Solutions
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3PCh. 19.1 - Prob. 19.4PCh. 19.1 - Prob. 19.5PCh. 19.1 - A 20-lb block is initially held so that the...Ch. 19.1 - Prob. 19.7PCh. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9PCh. 19.1 - A 5-kg fragile glass vase is surrounded by packing...
Ch. 19.1 - Prob. 19.11PCh. 19.1 - Prob. 19.12PCh. 19.1 - Prob. 19.13PCh. 19.1 - Prob. 19.14PCh. 19.1 - Prob. 19.15PCh. 19.1 - Prob. 19.16PCh. 19.1 - Prob. 19.17PCh. 19.1 - Prob. 19.18PCh. 19.1 - Prob. 19.19PCh. 19.1 - Prob. 19.20PCh. 19.1 - A 50-kg block is supported by the spring...Ch. 19.1 - Prob. 19.22PCh. 19.1 - Two springs with constants k1and k2are connected...Ch. 19.1 - Prob. 19.24PCh. 19.1 - Prob. 19.25PCh. 19.1 - Prob. 19.26PCh. 19.1 - Prob. 19.27PCh. 19.1 - From mechanics of materials it is known that when...Ch. 19.1 - Prob. 19.29PCh. 19.1 - Prob. 19.30PCh. 19.1 - Prob. 19.31PCh. 19.1 - Prob. 19.32PCh. 19.1 - Prob. 19.33PCh. 19.1 - Prob. 19.34PCh. 19.1 - Using the data of Table 19.1, determine the period...Ch. 19.1 - Prob. 19.36PCh. 19.2 - Prob. 19.37PCh. 19.2 - Prob. 19.38PCh. 19.2 - A 6-kg uniform cylinder can roll without sliding...Ch. 19.2 - A 6-kg uniform cylinder is assumed to roll without...Ch. 19.2 - Prob. 19.41PCh. 19.2 - Prob. 19.42PCh. 19.2 - A square plate of mass m is held by eight springs,...Ch. 19.2 - Prob. 19.44PCh. 19.2 - Prob. 19.45PCh. 19.2 - Prob. 19.46PCh. 19.2 - Prob. 19.47PCh. 19.2 - Prob. 19.48PCh. 19.2 - Prob. 19.49PCh. 19.2 - Prob. 19.50PCh. 19.2 - A thin homogeneous wire is bent into the shape of...Ch. 19.2 - A compound pendulum is defined as a rigid body...Ch. 19.2 - Prob. 19.53PCh. 19.2 - Prob. 19.54PCh. 19.2 - Prob. 19.55PCh. 19.2 - Two uniform rods each have a mass m and length I...Ch. 19.2 - Prob. 19.57PCh. 19.2 - A 1300-kg sports car has a center of gravity G...Ch. 19.2 - A 6-lb slender rod is suspended from a steel wire...Ch. 19.2 - A uniform disk of radius r=250 mm is attached at A...Ch. 19.2 - Two uniform rods, each of weight W=24 lb and...Ch. 19.2 - Prob. 19.62PCh. 19.2 - Prob. 19.63PCh. 19.2 - Prob. 19.64PCh. 19.2 - Prob. 19.65PCh. 19.2 - A uniform equilateral triangular plate with a side...Ch. 19.2 - Prob. 19.67PCh. 19.2 - Prob. 19.68PCh. 19.3 - Prob. 19.69PCh. 19.3 - Prob. 19.70PCh. 19.3 - Prob. 19.71PCh. 19.3 - Prob. 19.72PCh. 19.3 - Prob. 19.73PCh. 19.3 - Prob. 19.74PCh. 19.3 - Prob. 19.75PCh. 19.3 - Prob. 19.76PCh. 19.3 - A uniform disk of radius r and mass m can roll...Ch. 19.3 - Prob. 19.78PCh. 19.3 - Prob. 19.79PCh. 19.3 - Prob. 19.80PCh. 19.3 - A slender 10-kg bar AB with a length of l=0.6 m is...Ch. 19.3 - Prob. 19.82PCh. 19.3 - Prob. 19.83PCh. 19.3 - Prob. 19.84PCh. 19.3 - A homogeneous rod of weight W and length 2l is...Ch. 19.3 - Prob. 19.86PCh. 19.3 - Prob. 19.87PCh. 19.3 - Prob. 19.88PCh. 19.3 - Prob. 19.89PCh. 19.3 - Prob. 19.90PCh. 19.3 - Two 6-lb uniform semicircular plates are attached...Ch. 19.3 - Prob. 19.92PCh. 19.3 - The motion of the uniform rod AB is guided by the...Ch. 19.3 - Prob. 19.94PCh. 19.3 - Prob. 19.95PCh. 19.3 - Prob. 19.96PCh. 19.3 - Prob. 19.97PCh. 19.3 - Prob. 19.98PCh. 19.4 - Prob. 19.99PCh. 19.4 - Prob. 19.100PCh. 19.4 - Prob. 19.101PCh. 19.4 - Prob. 19.102PCh. 19.4 - Prob. 19.103PCh. 19.4 - Prob. 19.104PCh. 19.4 - Prob. 19.105PCh. 19.4 - Prob. 19.106PCh. 19.4 - Prob. 19.107PCh. 19.4 - The crude-oil pumping rig shown is driven at 20...Ch. 19.4 - Prob. 19.109PCh. 19.4 - Prob. 19.110PCh. 19.4 - Prob. 19.111PCh. 19.4 - Prob. 19.112PCh. 19.4 - Prob. 19.113PCh. 19.4 - Prob. 19.114PCh. 19.4 - Prob. 19.115PCh. 19.4 - Prob. 19.116PCh. 19.4 - Prob. 19.117PCh. 19.4 - Prob. 19.118PCh. 19.4 - Prob. 19.119PCh. 19.4 - Prob. 19.120PCh. 19.4 - Prob. 19.121PCh. 19.4 - Prob. 19.122PCh. 19.4 - Prob. 19.123PCh. 19.4 - Prob. 19.124PCh. 19.4 - Prob. 19.125PCh. 19.4 - A small trailer and its load have a total mass of...Ch. 19.5 - Prob. 19.127PCh. 19.5 - Prob. 19.128PCh. 19.5 - Prob. 19.129PCh. 19.5 - Prob. 19.130PCh. 19.5 - Prob. 19.131PCh. 19.5 - Prob. 19.132PCh. 19.5 - Prob. 19.133PCh. 19.5 - Prob. 19.134PCh. 19.5 - Prob. 19.135PCh. 19.5 - Prob. 19.136PCh. 19.5 - Prob. 19.137PCh. 19.5 - A 0.9-kg block B is connected by a cord to a...Ch. 19.5 - Prob. 19.139PCh. 19.5 - Prob. 19.140PCh. 19.5 - Prob. 19.141PCh. 19.5 - Prob. 19.142PCh. 19.5 - Prob. 19.143PCh. 19.5 - Prob. 19.144PCh. 19.5 - Prob. 19.145PCh. 19.5 - Prob. 19.146PCh. 19.5 - Prob. 19.147PCh. 19.5 - Prob. 19.148PCh. 19.5 - A simplified model of a washing machine is shown....Ch. 19.5 - Prob. 19.150PCh. 19.5 - Prob. 19.151PCh. 19.5 - Prob. 19.152PCh. 19.5 - Prob. 19.153PCh. 19.5 - Prob. 19.154PCh. 19.5 - Prob. 19.155PCh. 19.5 - Prob. 19.156PCh. 19.5 - Write the differential equations defining (a) the...Ch. 19.5 - Write the differential equations defining (a) the...Ch. 19 - Prob. 19.159RPCh. 19 - Prob. 19.160RPCh. 19 - Prob. 19.161RPCh. 19 - Prob. 19.162RPCh. 19 - Prob. 19.163RPCh. 19 - Prob. 19.164RPCh. 19 - A 4-lb uniform rod is supported by a pin at O and...Ch. 19 - Prob. 19.166RPCh. 19 - Prob. 19.167RPCh. 19 - Prob. 19.168RPCh. 19 - Prob. 19.169RPCh. 19 - Prob. 19.170RP
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.Similar questions
- Q.4 A device to produce vibrations consists of the two counter-rotating wheels, each carrying an eccentric mass mo = 1 kg with a centre of mass at a distance e = 12 mm from its axis of rotation. The wheels are synchronized so that the vertical positions of the unbalanced masses are always identical. The total mass of the device is 10 kg. For an equivalent spring stiffness of 900 kN/m, determine the amplitude of the force transmitted to the fixed mountings due to the imbalance of the rotors at a speed of 1500 rev/min. Neglect damping. mo mo wwwwarrow_forwardA 6-kg uniform cylinder can roll without sliding on a horizontal surface and is attached by a pin at point C to the 4-kg horizontal bar AB. The bar is attached to two springs, each having a constant of k = 4.2 kN/m, as shown. The bar is moved 12 mm to the right of the equilibrium position and released. Determine the period of vibration of the system. (Round the final answer to three decimal places.) The period of vibration of the system is ___s.arrow_forwardProblem 2.154: Critically Damped Torsional Vibration The needle indicator of an electronic instrument is connected to a torsional viscous damper and a torsional spring. If the rotary inertia of the needle indicator about its pivot point is 25 kg-m² and the spring constant of the torsional spring is 100 N-m/rad, determine the damping constant of the torsional damper if the instrument is to be critically damped.arrow_forward
- 2) A massless bar of length L carrying a tip mass m is rigidly connected to a homogenous disk of radius R and mass m as shown below. The disk rolls without slipping on the ground. Note that gravity acts down and that a spring of stiffness k and a dashpot of constant c connect the center of the disk to an oscillating wall and a fixed one respectively. Determine the amplitude of response of the angle 0(t).arrow_forwardQ.1 The system shown below consists of a block of mass m and a cylinder of mass 2m. The block and the cylinder are joined by pulley arrangement as show. The coordinates x and y are dependent in which x = 2y. Use m= 2 kg. The angle 0 is any value between 0 and 90°. If the cylinder is pushed downward 20 mm and released a) find the subsequent response of the block, x(1) b) find the displacement and velocity of the block at t = 1 s. The specific value of k is given in separate excel sheet. K=1985 2m IT, x = 2yarrow_forwardTwo 40-g weights are attached at A and B to the rim of a 1.5-kg uniform disk of radius r = 100 mm. Determine the frequency of small oscillations when β = 60°.arrow_forward
- The 8-kg uniform bar AB is hinged at C and is attached at and A to a spring of constant==k = 500 N/m. If end A is given a small displacement and released, determine (a) the frequency of small oscillations, (b ) the smallest value of the spring constant k for which oscillations will occur.arrow_forwardProblem 5.1 A rotational spring-mass system is shown to the right. The slender rigid bar has a mass of 18 kg and a length of { = 1.5 m. The springs have stiffness k = 360 N/m. The bar has a displacement of –0.06 rad and a speed of –1.1 rad/s when a harmonic moment M (t) = (80 N·m)cos 16t is applied. Find the response of the system. Assume small displacements. You will need to solve the differential equation because the results from lecture and in the book are for M(t) = M sin wt, not M (t) = Mo cos wt. You do not have to derive the homogeneous solution from scratch; you may use equations from Module 3, but the coefficients will be different. k - 3 Мо cos ot Answer: 0 (t) = {0.0540 cos 10t – 0.110 sin 10t 0.114 cos 16t} rad karrow_forwardAs shown in the Fig. 3, the CM of a cylinder of mass m and radius R is connected to the top of hoop of mass m by a spring. The spring constant is assumed to be known and it is denoted by k. At a given moment the system is slightly compressed and then suddenly released. After the release, both rigid objects roll without slipping. Determine the angular frequency of the resulting oscillation. It is assumed that the spring remains horizontal throughout the motion. Figure 3: Coupled Oscillatorarrow_forward
- A simplified model of a washing machine is shown. A bundle of wet clothes forms a weight wb of 20 lb in the machine and causes a rotating unbalance. The rotating weight is 40 lb (including wb) and the radius of the washer basket e is 9 in. Knowing the washer has an equivalent spring constant k = 70 lb/ft and damping ratio and during the spin cycle the drum rotates at 250 rpm, determine the amplitude of the motion and the magnitude of the force transmitted to the sides of the washing machine.arrow_forwardWant in detailarrow_forwardTwo masses m1 and m2 each connected by two springs of stiffness k, are connected by a rigid massless horizontal rod of length l as shown in Fig. 5.22. (a) Derive the equations of motion of the system in terms of the vertical displacement of the C.G. of the system, x(t), and the rotation about the C.G. of the system, θ(t) (b) Find the natural frequencies of vibration of the system for m1=50 kg, m2=200 kg and k = 1000 N/m.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Undamped Free Vibration of SDOF (1/2) - Structural Dynamics; Author: structurefree;https://www.youtube.com/watch?v=BkgzEdDlU78;License: Standard Youtube License