Mechanical system consists of: body 1 of mass m m; body 3 - two-stage disk of mass m 6m, radiir and R=2r, and R. radius of inertia i= toward horizontal axes passing through its center: both bodies 4- equal horizontal springs cach of coe- icient of elasticity c. An ideal cord 2 connects body 1 and body 3. Disk 3 moves by its small drum on a fixed horizontal plane without sliding. At the initial moment system is turned out of its equilibrium by small shifting of magnitude x of the body 1 in the x direction (according to the ligure) and released with initial velocity of magnitude v. Assuming the system makes small oscillations around its equilibrium, neglecting resistance forces, and m,r.c are positive constants, find: a) kinetic energy of the system; b) total power of the forces acting upon the system; c) differential equation of the system motion (using the body I motion at x direction); d) the law of the system motion (using the body 1 motion at x direction). www

Mechanical system consists of: body 1 of mass m m; body 3 - two-stage disk of mass m 6m, radiir and R=2r, and R. radius of inertia i= toward horizontal axes passing through its center: both bodies 4- equal horizontal springs cach of coe- icient of elasticity c. An ideal cord 2 connects body 1 and body 3. Disk 3 moves by its small drum on a fixed horizontal plane without sliding. At the initial moment system is turned out of its equilibrium by small shifting of magnitude x of the body 1 in the x direction (according to the ligure) and released with initial velocity of magnitude v. Assuming the system makes small oscillations around its equilibrium, neglecting resistance forces, and m,r.c are positive constants, find: a) kinetic energy of the system; b) total power of the forces acting upon the system; c) differential equation of the system motion (using the body I motion at x direction); d) the law of the system motion (using the body 1 motion at x direction). www

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

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Determine the equivalent spring constant of the system where the spring will be located in the position of k1. k1=1N/m, k2=5N/m (answer in N/m)
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PROBLEM 3 WY ↓x R Mechanical system consists of: body 1 of mass mm; body 3 - two-stage disk of mass my-2m, radii r and R=2r, and radius of inertia i,- toward horizontal axes passing through its center; both bodies 4-equal horizontal springs each of coe- fficient of elasticity c. An ideal cord 2 connects body 1 and body 3. Disk 3 moves by its small drum on a fixed horizontal plane without sliding. At the initial moment system is turned out of its equilibrium by small shifting of magnitude x, of the body 1 in the x direction (according to the figure) and released with initial velocity of magnitude vo. Assuming the system makes small oscillations around its equilibrium, neglecting resistance forces, and m, r, c are positive constants, find: a) kinetic energy of the system; b) total power of the forces acting upon the system; c) differential equation of the system motion (using the body 1 motion at x direction); d) the law of the system motion (using the body 1 motion at x direction).
3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.
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-
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The sketch below shows two thin, uniform bars, 2 and 3, connected to one another and the fixed frame, 1, by revolute joints at A and B. At first, the system is stationary with 2 and 3 oriented vertically below point A. A counterclockwise torque, T, is then applied to body 3. 1 A 2 3 Side view of two bars at t = 0 Body 2 is characterized by length L2, mass m2, and centroidal mass moment of inertia m2 (L2)? Body 3 is characterized by length L3, mass m3, and centroidal mass moment of inertia m3 (L3)? a) Sketch the free body diagrams of both bodies b) Sketch the FBD for the instant when T is applied c) Determine the force(s) exerted on 2 by 1 at A d) Determine the force(s) exerted on 3 by 2 at B e) Determine the angular acceleration of 2 f) Determine the angular acceleration of 3.
A four-wheeled vehicle of total mass 5000 kg has two pairs of wheels of 500 mm radius. Each pair of wheels with axles has mass of 750 kg, the radius of gyration of each wheel being 400 mm. The axles are 2 metres apart and the c.g. of vehicle is mid-way at a height of 1-2 m above the road surface. Find the reactions of the front and rear wheels, if tractive force of 6 kN is acting 50 mm below the centre of gravity of vehicle.
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.
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
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