b. Find the equation of motion of the system below using Lagrange's equation. Masses m₁,m2, and m3 are added to the compound pendulums with rod masses Mr₁, Mr2, andMr31respectively. Assume the mass of all pendulums are evenly distributed so that their centerof gravity is in the middle of the pendulum of length L. Use the small angle assumption.O○L02M1Lm3m2

All the parts are solved properly with detailed explanation.Hope you got your answer. If any query…

Answered: b. Find the equation of motion of the…

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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A block of mass m1 is located on an inclined plane θ and attached by a rope passing over a pulley with a weight of mass m2. If m1 > m2 find the tension and the acceleration.
The shaft, bearing two unbalanced masses, rotates at a constant speed of ω = 20 r/s. In the case of balancing in the DI and DII planes, find the balancing values (kg.mm) and their positions.
A conical pendulum having a 2 kg massattached at the end of the string is rotating ata constant speed of 4.00 m/s around ahorizontal circle of radius 1.00 m. Calculate(a) the angle that the string makes with thevertical;(b) the tension in the string; and(c) the length of the string.
A helical spring has a stiffness of of 25 kN/m. If a mass of 100 kg is attached to its free end, pulled down, and then released, (a) amount of deflection, in cm, (b) determine the periodic time of its motion. (c) If the maximum deflection was 50 mm, find the velocity and acceleration of the mass when it is 300 mm from the equilibrium position. Make an illustration.
A, B, C and D are four masses carried by a rotating shaft at radii 100mm, 150mm, 150mm and 200mmrespectively. The planes in which the masses rotate are spaced at 500mm apart and the magnitude ofthe masses B, C and D are 9kg, 5kg and 4kg respectively. Find the required mass A and the relativeangular settings of the four masses so that the shaft shall be in complete balance.
A spring-based toy gun is used to shoot a ball of mass M straight up.The ball is not attached to the spring. The ball is pushed downward into the spring so that the spring is compressed toa distance S below its relaxation point. After the release, the ball reaches a maximum height 3S,measured from its relaxation position, see Fig. 1(b). (a) Find the constant of the spring. (b) Findthe equilibrium point of the ball when it is on the compressed spring with no forces other than gravity and thespring acting on it. Clearly indicate the point you are using as the origin of your coordinate system and which direction is positive.system and which direction is positive. (c) Now the ball is glued to the spring so that it oscillates up and downinstead of flying off the spring. The spring is again compressed to the same distance S below itsof relaxation. Write an equation for the position of the ball as a function of time after it is released. Indicateclearly which point you are using as the origin…
The pulley in Fig has radius R and a moment of inertia I. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the tabletop is mk . The system is released from rest, and block B descends. Block A has mass mA and block B has mass mB . Use energy methods to calculate the speed of block B as a function of the distance d that it has descended.
If either a simple or a compound pendulum is used to determine experimentally the acceleration of gravity g, difficulties are encountered. In the case of the simple pendulum, the string is not truly weightless, while in the case of the compound pendulum, the exact location of the mass center is difficult to establish. In the case of a compound pendulum, the difficulty can be eliminated by using a reversible, or Kater, pendulum. Two knife edges A and B are placed so that they are obviously not at the same distance from the mass center G, and the distance l is measured with great precision. The position of a counterweight D is then adjusted so that the period of oscillation τ obtained is equal to that of a true simple pendulum of length l and that g 4π2 l/τ.
If the speed of the shaft, as shown in Figure 1 below, is 220 rev/min, calculate the magnitudes and orientations of the bearing reactions at A and B for the two-mass system. Given a = b = 250 mm, c = 50 mm, R1 = 60 mm, R2 = 40 mm, m1 = 2 kg, and m2 = 1.5 kg.
A uniform rod of mass M = 2.3 kg and length L = 0.2 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by 1/3 ML2. If a force F = 7 N, q = 47° acts as shown, what is the resulting angular acceleration (in rad/s2) about the pivot point?
a) In the Fig Q4(in the attatched image) shows a system of four unbalanced masses. Determine the bearing reactions if the rotor speed is 600 r.p.m.
Engineering Dynamics need help with 4,5,6,7 A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°. Neglect any friction. Neglect also the size of the ball and the thickness of the arm. Find the relationship between r, R and θ where r is the distance between O and the ball. Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA. Write the equations of motion in the (r, θ) coordinate system. Find the normal force acting on the ball by the cylinder for Φ = Φ0. Find the normal force acting on the ball by the bar for Φ = Φ0. Determine the angle Φ at which the ball loses contact with the cylinder. Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°

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