h2G1G2L1m2, k2m1, k1Fig QaFig QbTwo compound pendulums of lengths L1 and L2 are pivoted at a support andconnected together through a horizontal spring of stiffness k as in Fig Qa. Themasses and radii of gyration of the pendulums about the centres of mass (G1 andG2) are ml & m2 and kl & k2 respectively. The centres of mass are at distanceshl and h2 respectively whilst the spring is distance I from the pivots as shown.The pendulums are set into motion by small displacements xl and x2 opening upsmall 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 mi = 10 kg.m2 = 8 kg, kı = 0.433 m, k2. = 0.3464 m, L1= 1.2 m, L2. = 1.0 m, hı= 0.6 m, h.. = 0.5 m,1=0.8 m, and k=2000 N/m.

The dimensions of the object in suspension in a simple pendulum are much lower than the distance…

Answered: h2 G2 G1 L1 X2 m2, k2 Fig Qa Fig Qb m1,…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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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 mass m₁ = 2.0 kg is suspended over a pulley of moment of inertia, I₁ = 0.010 kg-m², and a radius, R₁ = 0.10 m, and is attached with a massless rope to a mass on a horizontal table, m₁ = 2.0 kg. This mass is itself attached to another suspended mass m₂ = 4.0 kg again with a massless rope over a pulley of moment of inertia, I₂ = 0.040 kg-m², and a radius, R₂ = 0.20 m. (a) Find the velocity of each mass when my falls a distance of 1.00 m (the masses start at rest). (b) There is now friction on the horizontal table, µ = 0.74. Again find the velocity of each mass when my falls a distance of 1.00 m (the masses still start at rest).
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11 A cylinder of mass m and mass moment of inertia J is free to roll without slipping, but is restrained by the spring k, as shown in Fig. P2-11. Determine the natural frequency of oscillation. Use:force balance method m. Jo k
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Q1: In the below drawings, three unbalanced masses and related details are provided. Please answer the following questions. a) a balancing mass is to be located at rp = 50 mm, then what would be the balancing m1 m1 650 mm 200 mm m2 mass (m,) and its angular position (Op) (Please use the r2 m2 A graphical method) r3 m3 15 m3 b) If the system is not balanced what would be the reaction forces at A and B. (FA, FB=?) n = 150 rpm r; = 30 mm m, = 1 kg r2 = 20 mm 40 тm 13= m, =3 kg m; = 2 kg k = please choose an appropriate scaling factor yourself SHOT ON MI 6 MI DUAL CAMERA
2. Determine the number of degrees of freedom necessary for the analysis of the system shown in the figure below. 0.1L 0.4L+ 0.3LS-+ 0.2L 2k G 2k Slender rod of mass m m2 moment of inertia I
A homogeneous slender bar AB of mass m and length L is released from rest in the position shown in figure below. Assuming that the horizontal plane is frictionless. 1.) Draw the free body diagram and say how many forces act on the bar and which force is doing the work. 2.)Draw the kinematic diagram and show how manoy vectors act on the bar. 3.) Draw the kinetic diagram and show how many inertia-term vectors act on the bar.
The figure below shows an assembly consists of a thin rod ( mass 1.4 kg and length 1 m) and two spheres ( top and bottom) with m;=0.2 kg, R1=0.1 m and m2=0.3 kg, R2=0.3 m. If the assembly is free to rotate around point O, the moment of inertia of the assembly in kgm2 is 2 ( Icom, rod = 1 ML2 , Icom,sphere=mR2) 12 R1 Sphere 1 Rod L/2 R2 Sphere 2
A flywheel of mass 0.7 ton is fitted to a multi cylinder engine, which runs at a mean speed of 310 r.p.m. If the speed varies from 6 % above the mean to 3 % below it and the fluctuation energy is 2000 kN-cm, find @ mass moment of inertia of the wheel and (i) radius of Gyration. The mass moment of Inertia in Kgm: is Radius of Gyration in m is
A solid disc with radius R is connected to spring at point (d) distance above the center of disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of disc is (M) and the spring constant is (K). The polar moment of inertia for disc about its center is J = 1/2MR2 , so the natural frequancy for the system is 1 2K(R+d)² MR2 the Answer is O 1 2K 2п 3M
Gravitational acceleration g = 10 m/s? 1. A uniform thin rod of length Im and mass m,od = 20 Kg in the figure can rotate freely in the plane about an axis at 30 cm from one of its ends while the other end attached with a disk of radius 10 cm and mass maisk = 10 Kg. As the rod swings from the angle 30". a. Find the position center of mass. b. Calculate the moment of inertia for the composed system. c. What is the velocity of the disk while reaching an equilibrium point? 30 cm

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