Problem 3: Consider the pendulum shown below that oscillates about the pivot point O. Assume that the mass of the rigid bar of length L3 is negligible. Determine the linearized equation of motion with respect to the angular displacement 6(t) of the pendulum. L1 L2 L3

Problem 3: Consider the pendulum shown below that oscillates about the pivot point O. Assume that the mass of the rigid bar of length L3 is negligible. Determine the linearized equation of motion with respect to the angular displacement 6(t) of the pendulum. L1 L2 L3

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

Related questions

Q: An aeroplane runs at 600 km/h the rotor of the engine weighs 4000 N with radius of gyration of 1…

Q: 1/ The acceleration of an oscillating mass on a spring is greatest when passing the equilibrium…

A: This statement is (FALSE)

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

Q: Find the resultant reaction at each bearing due to the mass and gyroscopic effects for a uniform…

Q: A 1. A rigid bar, of length L and constant mass per unit length m = m/L, is pinned to a stationary…

Q: HW2 A uniform disc of 80 mm radiuse has a mass of 2000 g. It is mounted centrally in bearings which…

A: Given d=80mm r= 40mm = 0.04m m= 2000g = 2kg N=550rpm…

Q: A 25 kg mass is resting on a spring of 4900 N/m and dashpot of 147 N-se/m in parallel. If a velocity…

Q: A rotor of 75 mm radius has a mass of 5 kg. It is mounted centrally in bearings which maintain its…

A: Given data r= 75mm, m=5kg, N= 600rpm…

Q: A uniform rigid bar of mass that is pivoted at point O and connected by springs of stiffnesses kl…

Q: Find the equation of motion of the system where G is mass center and e is the distance to the…

Q: A light inextensible string has one end attached to a fixed support A. The other end is attached to…

Q: A rod of mass M and length L is pivoted at point O, as shown below. At the end f each rod is a…

Q: Problem 3. Determine the equations of motion and the number of degrees of freedom. Mass of the…

Q: Derive the differential equation of motion for the system shown in Figure (). Neglact the mass of…

Q: Example 1: A uniform disc of 150 mm diameter has a mass of 5 kg It is mounted centrally in bearings…

A: Solution : Given data d = 150 mm m = 5 kg N = 1000 rpm Np = 60 rpm l = 100 mm = 0.7m…

Q: System is shown. mass=M Length = L Uniform rod is pivoted about one end and oscillates in a…

A: givenmass of uniform rod=Mlength of uniform rod =Lone place a mass m=M

Q: 2. A uniform bar of length 2a, and mass m is linked to a uniform cylinder of radius b and mass M. In…

A: Given, The length of bar, L = 2a The radius of cylinder, r = b The mass of cylinder, m = M

Q: Problem 3. Determine the equations of motion and the number of DOF for the system. K3 K4 m2 K1 K2 m1

Q: HW1 A uniform disc of 220 mm in diameter has a mass of 3.5 kg. It is mounted centrally in bearings…

Q: Develop the equation of motion in terms of the variable x for the system shown Draw free body…

Q: A uniform disc of 220 mm diameter has a mass of 3.5 kg. It is mounted centrally in bearings which…

Q: Example 1: A uniform disc of 150 mm diameter has a mass of 5 kg. It is mounted centrally in bearings…

Q: Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and…

A: Compound pendulum: When any rigid body starts oscillating due to the effect of the force of gravity…

Q: A pendulum consisting of a rod of mass 2m of mass 3kg and a ball of mass 1kg and a radius of 0.3m…

Q: Five (5) uniform discs of mass 5 kg each are fitted onto a shaft which is rotating at 3,000 rpm…

Q: The mass of a turbine rotor of a ship is 8000 kg and has a radius of gyration of 0.75 m. It rotates…

A: The sloution is given below

Q: - The flywheel of an engine driving a dynamo has a mass of 180 kg and a radius of gyration of 30 mm.…

A: Given: Flywheel mass = 180 kg radius of gyration = 30 mm effective length = 250 mm diameter = 50…

Q: A circular cylinders of radius r and mass m is connected by two springs, as shown below. Derive the…

Q: Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and…

Q: (97) Derive the equations of motion of the system shown in the figure below using Lagrange's…

A: To derive: The equation of motion using Lagrange's equation. Given: The mass of the circular…

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

Q: In the figure below, the disc has mass m = 82.2998 kg, radius r= 6.7128 m, and moment of inertia…

A: Given data: The angular acceleration of the disc can be shown as, The angular velocity of the disc…

Q: HW3 A uniform disc of a 90 mm radius has a mass of 2500 g. It is mounted centrally in bearings that…

Q: A uniform disc of 80 mm radiuse has a mass of 2000 g. It is mounted centrally in bearings which…

Q: The 3.0 kg pendulum with mass center G is pivoted at A to the ficed support CA. It has a radius of…

Q: h2 G2 G1 L1 X2 m2, k2 Fig Qa Fig Qb m1, k1 Two compound pendulums of lengths L1 and L2 are pivoted…

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

Q: 2. A uniform bar of length 2a, and mass m is linked to a uniform cylinder of radius b and mass M. In…

A: Now by using torque method, equating all the torques:

Q: The moment of inertia of a pair of locomotive driving wheels with the axle is 150 kg.m². The…

A: To find: The gyroscopic couple produced. Given : The moment of inertia of wheel is I= 150 kg·m2. The…

Q: The static equilibrium position of a massless rigid bar, hinged at point O and connected with…

Q: The thin rod of the figure has a mass of 15kg and is attached to a spring of constant K = 50 N/m at…

Q: Draw the free-body diagram and derive the equation of motion using Newton's second law of motion for…

A: Given: To determine: Equation of motion

Q: Find the radius of gyration (KG) of a compound pendulum if the time period (T) is 1.5 second and…

Q: HW2 A uniform disc of 80 mm radius has a mass of 2000 g. It is mounted centrally in bearings that…

Q: A simple pendulum is pivoted at O and is free to swing in the vertical plane of the plate. If the…

A: Given data: a=3.7 m/s2θ=34° Need to determine the value of the angle "β".

Q: Exercise 30: A uniform and homogenous rod (R) of length L=100cm and mass m=lkg is free to rotate…

Q: The accelerating torque increases the speed of a flywheel from x rpm to y rpm in 15 seconds. Find 1.…

Q: Q1: A machine is modelled by the system shown. The masses of the main elements and m2, and the…

Concept explainers

Project Management Techniques

The guideways or the roadways that are undertaken to perform a project efficiently and all the tools required to accomplish the task are the general outlines for project management techniques.

Question

Please find the question attached.

Problem 3:
Consider the pendulum shown below that oscillates about the pivot point O. Assume that the
mass of the rigid bar of length L3 is negligible. Determine the linearized equation of motion
with respect to the angular displacement 6(t) of the pendulum.
L1
L2
L3

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

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

Determine the motion expressions for each of the systems shown below by using the Euler-Lagrange equation. not skiping steps please explain i do not understand yet Pendulum of length (l) and mass (m) whose support rotates in a circle of radius (a) in a vertical plane, with constant angular velocity ω as shown in the figure
The disk in the system shown below rolls without slip on the plate. Using x, the displacementof the plate from the system’s equilibrium position, as the generalized coordinate. Specifythe following:a. The equation of motionb. The natural frequency
The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2 . Calculate the natural frequency (in radian/s) of the compound pendulum.
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.
A uniform density stick of length L oscillates as a physical pendulum. It is pivoted a distance x from the center of mass, as shown in the diagram. Find the expression for the angular frequency as a function of the distance x between the pivot point and the center of mass of the stick
A shaft is rotating at a uniform angular speed. Four masses M1, M2, and M3 and M4 of magnitudes 300kg, 450kg, 360kg, 390kg respectively are attached rigidly to the shaft. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250mmand 300mm respectively. The angle made by these masses with horizontal are 0°.45°, 120°and 255°respectively. Find-(i) the magnitude of balancing mass (ii) the position of balancing mass if its radius of rotation is 200mm.
A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.
Consider the slider-crank mechanism shown. Crank AB is 0.500 m long and is rotating counterclockwise at 3.00 rad/s. Rod BD is 1.500 m long. 1. Which of the following gives the closest value of the speed of end B of crank AB? 2. If crank AB is rotating at a constant angular velocity, which body/bodies is/are in general plane motion?
In a spring controlled governor, mass of each ball of governor is 7 kg and moves radially under the action controlling force E. If the speed range is 420 rpm and 44 rpm with a range of ball path radius r equal to 12.4 cm to 13.2 cm. determine the linear relationship between ball path rudius and controlling force sketch te Grati between F and r. What in the equilibrium speed at r= 12.8 cm?
A simple pendulum is pivoted at O and is free to swing in the vertical plane of the plate. If the plate is given a constant acceleration a = 4.2 m/s2 up the incline θ = 30°, find the steady angle β assumed by the pendulum after all initial start-up oscillations have ceased. Neglect the mass of the slender supporting rod.
Determine the governing equation of motion for the system shown below as well as zeta, wn and tau D.
gine driving a dynamo has a mass of 180 kg and a radius of gyration of 30 mm. The shaft at the flywheel end has an effective length of 250 mm and is S0 mm diameter. The armature mass is 120 kg and its radius of gyration is 22.5 mm. The dynamo shaft is 34 mm diameter and 200 mm effective length. Calculate the position of node and frequency of torsional oscillation. G = 83 kN/mm?>.