The homogeneous circular disk shown in Figure A3.4 has mass moment of inertia about its centre ofmass of l = 3 kgm². It rotates about a fixed shaft at its centre and is attached to a torsional springwith constant k = 20 Nm/rad.At t = 0, the angle is = 0, the angular velocity is d/dt = 4 rad/s, and the disk is subjected to anoscillatory couple M(t) = 10 sin 2t Nm.Determine as a function of time..Figure A3.4M(1)

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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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Problem 2 Consider the blodk of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle a. Let l be the length of the spring at equili brium, and a be the elongation. The block oscillates and at the same time is rotating around origin O, in the plane of the inclined, by a variable angular velocity . 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa tions) reference plane
Problem 2 Consider the block of mass m, connected to a spring of spring constant k and placed on a inclined plane of angle equili brium, and r be the elongation. The block oscillates and at the same time is rotating around origin 0, in the plane of the inclined, by a variable angular velocity . Let l be the length of the spring at 1. Calculate the degrees of freedom of the block 2. What is the kinetic energy of the block 3. What is the potential energy of the block 4. Write the Lagrangian function (don't derive the Euler Lagrange equa- tions) reference plane m
FOR FIG REFER THE ATTACHED IMAGE The shaft is massless. A thin attached triangular mass ‘m’ is mounted on the shaft. Rotational speed of the shaft is ω. Neglect weight effect of attached mass. Bearings are at A and B. Take Z- axis along the shaft axis. X- axis is vertically downward. Y – axis is horizontal. Take origin at mid-point on the shaft. Question: Under what practical condition can we justify the neglecting of weight of the attached triangular body?
Consider the mechanical system of this figure comprising two wheels of mass m, inertia j, andthree springs each of stiffness k. The wheels move on two fixed horizontal surfaces during thesystem's free vibrations. Derive the mathematical model of this mechanical system.
QUESTION 4 (a) With the aids of diagram, explain how gyroscopic moment is generated. (b) The thin disk of mass m kg and radius R shown in Figure Q4(b) rotates relative to the pivoted shaft AB of length L at constant angular speed . At the same instant, the entire assembly rotates at a constant angular speed of 2. Determine the relationship between the spin rate w and precession rate 2 so that the shaft AB is always in horizontal position (i.e. 0 = 90°) (c) Evaluate the angle 0 if the angular velocity of the disk is further increased? A 32 L Figure Q4(b) B J
Consider the system shown in the figure in which a harmonic force acts on the mass m. Derive the condition under which the steady-state displacement of mass m will be zero. Disc, mass M Rolls without slipping Pulley Cord Fo sin ot m
In the figure below, the unbalanced wheel O has a mass of 30 kg and is connected to a 20 kg counter weight block, B, with a continuous cable. If a constant moment of 15 N-m is applied to the wheel in the clockwise direction. At the instance shown, the angular velocity, w, is 4 rad/s. The center of mass, G is 5 cm from the center and the wheel's radius of gyration is 7 cm (about center point O). Assume the pulley is mass-less and frictionless. M 5 cm 5 cm Calculate the angular acceleration
A uniform thin rod shown in Figure 1, has a mass of 2 kg and carries a concentrated mass of 2.5 kg at B. The rod is hinged at A and is maintained in the horizontal position by a spring of stiffness 2 kN/m at C. Calculate the frequency of oscillation, neglecting the effect of the mass of the spring.
4. A student followed strictly correct procedure in the lab during the experiment of moment of inertia. He measured the mass and diameter of plastic cylinder with value of m = 0.36 kg and D = 0.1 m. The period of system without plastic cylinder is To = 0.667 s. The period of system with plastic cylinder T₁ = 0.92 s. Find: The spring constant K of the system. If a metallic cylinder and a plastic cylinder have same diameter and same thickness, which one has larger moment of inertia? Explain.
An undamped spring/mass system, in which m = 8 slugs and the spring constant k = 16 lb/ft has a driving force f(t) = t^pi*t on [0,pi] Extend f(t) into the negative t-axis to obtain an odd function. Find the particular solution ??(?). (Note: f(t) is given as half of the period, p = π.)
Consider the system shown at right. Find an equation of motion for the block with mass m,. Assume that the small wheel has negligible mass moment of inertia and that the larger one has a radius R and a mass moment of inertia I (measured respect to its axis of rotation). Note that there is a friction between the block with m2 mass m2 and the plane. The dynamic friction coefficient is equal to µa. m1 Md
0.5 m, k = 500 N/m, and k = 40 N.m/rad, In the system shown, m = 10 kg, r = 0.3 m, Ko where ko is the radius of gyration of the pulley about point 0. There is no slippage between the cord and the pulley. Replace the system with an equivalent { a) torsional spring and mass moment of inertia at point 0, and b) translational mass and spring at point A. т, Ко kt А k m ww

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