h2h1L2G2G1L1wwwwwwm2, k2m1, k1Fig 4aFig 4bFigure Q4 QUESTION 4Two compound pendulums 01 and 02 are pivoted at a support and connected together througha horizontal spring of stiffness k as in Fig. 4a. The masses and radii of gyration of thependulums about the centres of mass (G1 and G2) are m1 & m2 and kl & k2 respectively. Thecentres of mass are at distances hl and h2 respectively whilst the spring is distance I from thepivots as shown. The pendulums are set into motion by small displacements x1 and x2 openingup small angles 01 and 02 respectively as in Fig. 4b. Find the equations of motion of the twopendulums. Also determine the natural frequencies of the vibration of the pendulums if m1 =7.5 kg, m2. = 6 kg, kl = 0.433 m, k2. = 0.3464 m, L1 = 1.5 m, L2. = 1.2 m, h1 = 0.75 m, h2. =0.6 m, 1= 0.9 m, and k = 1600 N/m.

Given Datam1=7.5kgm2=6kgk1=0.433mk2=0.3464mL1=1.5mL2=1.2mh1=0.75mh2=0.6ml=0.9mk=1600N/m

Answered: Two compound pendulums 01 and 02 are…

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

See similar textbooks

Similar questions

A uniform solid cylinder with mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string (Fig.). The string doesn’t slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from rest.
A giant snowboard, represented by a rigid and slender rod with mass m and length L, slides on the undersized cylindrical half-pipe of radius r without friction at its ends A and B. The motion of the snowboard within the half-pipe occurs only within the vertical plane shown. Using the generalized coordinate 0, derive the equations of motion for this system using Lagrange's Equations. Note: The moment of inertia of a slender rod about its center of mass IG=1/12*m*L2 A C
The spring, Parts of a Vehicle weigh (9.79KN), sta center of gran'ty is (106.7cm) behind the front axle & wheelbam is (223.6cm) - The combined Stiffness of the Springs ot the front suspension is ( 24.52 kN/m) & that of the rear suspinsion is (26.27KN/m). The radius of ayration of the spruny a horizontal transverse axis through the center ot gravity is (102.6cm) .Calculate 'the natural freguemcies of the pitch & bounce motions of the vehicle Also de termine the locations ol osc;llatn bodg. parts about enters.
An elliptical hoop of negligible thickness with a vertical orientated semi-major axis a and a horizontal orientated semi-minor axis b, which has a mass per unit length of p, is mounted on a circular peg to which is attached a Carte- sian xy coordinate system in a vertical orienta- tion as shown in the accompanying sketch (the gravity g ellipse and peg are not rigidly joined to each other and are simply in kinematic contact with each other with negligible friction), such that the physical system lies within a flat ry plane. The ellipse is then allowed to freely oscillate in a to-and-fro rocking motion by a small angle 0, such that the gravitational acceleration g acts in a downwards direction that is parallel to the ellipse semi-major axis. 1.3 a 1.4 b Considering the above system determine the following information clearly showing all steps and appropriate reasoning: Y Utilizing the previously derived equation of motion determine the corresponding natural angular frequency wn for the…
Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and distance from point of suspension to center of gravity is “h”& is equal to 25 cm.
4. In order to determine the mass moment of inertia of a 4-foot diameter flywheel, the flywheel is tested\twice with different deadweight. In the first test a weight of 20 lb is attached by cord and observed to fall 10 ft in 4.6 seconds. In the second test a weight of 40 lb falls 10 ft in 3.1 seconds. Assuming that the torque due to bearing friction is constant, determine mass moment of inertia of the flywheel. Your solution must include W supporting FBDS.
Edit question Calculate the radius of gyration for the system of two tubes and a seat that form a swing with respect to the axis A shown in the figure. The dimensions of this system are shown in the figure below.The tubes have a mass of 19 kg/m. This means that each meter of tube has a mass of 19. Tubes can be thought of as slender rods.The seat has a mass of 23 kg and can be considered as a thin plate. Note that several views of the swing are offered so that you can better understand which is the reference axis A and the necessary dimensions. As you solve the problem, take into account that you are going to fill a table with the following format. It must be filled with the corresponding units.
Problem 4. A thin, semi-circular ring of mass m and radius R is pinned to ground at point O. The bar is released from rest in the position shown. Note that a = 2R, IG = mR² - ma² (a) Find the mass moment of inertia of the body about point O (b) Find the angular acceleration of the ring when released (c) Find the reaction forces on the ring at point O Ans: (b) a=0.5(g/R); (c) Ox = (mga)/(2R), Oy = mg/2 6.0 g G a -R-
dsphere dbar • Given the above system, two spheres attached to the ends of a cylinder, determine the mass moment of inertia about the axis normal to the page as a function of the variables provided. Note, you can treat the masses of each element of the system as known o (msphere and mbar). After deriving an expression for the mass moment of inertia about the axis normal to the page as a function of the variables, calculate the mass moment of inertia given: osphere properties ▪ mass of sphere = 5 kg 1 diameter of sphere = 0.5 m bar properties ▪ • Determine the resultant force and moment acting on the system if the system is moving as follows: mass of bar = 25 kg length of bar = 7.5 m diameter of bar = 0.25 m O a = 5î+ 2ĵ m/s² O αG = 7k rad/s² ασ
h2 L2 G2 G1 L1 www x2 www m2, k2 02 m1, k1 Fig Qa Fig Qb Two compound pendulums of lengths L1 and L2 are pivoted at a support and connected together through a horizontal spring of stiffness k as in Fig Qa. The masses and radii of gyration of the pendulums about the centres of mass (G1 and G2) are m1 & m2 and k1 & k2 respectively. The centres of mass are at distances hl and h2 respectively whilst the spring is distance 1 from the pivots as shown. The pendulums are set into motion by small displacements xl and x2 opening up small angles 01 and 02 respectively as in Fig Qb. 4.1 Find the equations of motion of the two pendulums. 4.2 Also determine the natural frequencies of the vibration of the pendulums if mı = 10 kg, m2 = 8 kg, kı = 0.433 m, k2. = 0.3464 m, L1 = 1.2 m, L2. = 1.0 m, hi = 0.6 m, h2. = 0.5 m, 1= 0.8 m, and k = 2000 N/m.
A rigid body is made of three identical thin rods, each of mass m and length L= 0.6 m,attached together in the form of an H. The body is allowed to fall from the horizontalposition, rotating around one of the legs of the H.a) What is the rotational inertia of the H, in terms of m and L?b) What will be the angular speed of the H when it is oriented vertically?

Recommended textbooks for you

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

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

SEE MORE TEXTBOOKS