In the system shown in Fig., AB is a massless rod which pivots freely about a pin connection at A. If the generalized coordinates are selected to be the angular orientation of the rod and the displacement of the second mass, obtain the differential equations of this system using Lagrange's equation. Use the assumption of small oscillations. B. m1 A k2 m2

In the system shown in Fig., AB is a massless rod which pivots freely about a pin connection at A. If the generalized coordinates are selected to be the angular orientation of the rod and the displacement of the second mass, obtain the differential equations of this system using Lagrange's equation. Use the assumption of small oscillations. B. m1 A k2 m2

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

Similar questions

For the system shown, determine: a) the differential equation of motion,b) The damping ratio, c) Equivalent mass and stiffness, d) Natural frequency ωn
An elastic string of natural length 4a is fixed at one end to a point O.its hangs vertically and carries at its other end a particle of mass 2m , In the position of equilibrium ,the length of the string is 5a Find, i)The modulus of elasticity of the string ii)The period of small vertical oscillations of the particle when it is pulled downward from its equilibrium position and then released
A body vibrating with viscous damping makes five complete oscillations per second, and in 10 cycles its amplitude diminishes by 1/5 of the orginal value. Determine the logarithmic decrement and the damping ratio.
A thin cylindrical rod of uniform mass m and length L is suspended from the ends by two massless springs with constants k1 and k2 (Distance L1 and L2 on either side of the center of mass of the rod). The motion of the center of mass is constrained to move up and down parallel to the vertical y-axis. It also experiences rotational oscillations around an axis perpendicular to the rod and passing through the center of mass (I is the moment of inertia with respect to said axis). be y1 and y2 the displacements of the two ends from their equilibrium positions, as shown in Fig. a) Find the motion's equation (consider k1=k2=k)
A 4-lb uniform rod is supported by a pin at O and a spring at A and is connected to a dashpot at B. Determine (a) the differential equation of motion for small oscillations, (b ) the angle that the rod will form with the horizontal 5 s after end B has been pushed 0.9 in. down and released.
Determine the steady-state amplitude of the mass center of the bar of Fig P6.3 when its right end is subject to a moment M=4000son105t N.m.
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.
A rigid and weightless rod is restricted to oscillations in the vertical plane as shown in the figure below.Determine the natural frequency of the system of mass m.
Derive the expression for motion and determine the natural frequency of the system shown in the figure below. Neglect the mass of the rod.
The mass m is attached to one endof a weightless stiff rod which isrigidly connected to the center of ahomogeneous cylinder of radius r, ifthe cylinder rolls without slipping, What is the natural frequency ofoscillation of the system?
A uniform rigid mass of 2 lb is hinged at its centre and laterally supported at one end by a spring of constant k=300 N/m. If the equation obtained for frequency (ωn) in this system is ωn2 =k/m, what is the natural frequency?
A turbine rotor of a ship is of 2000 kg mass and has a radius of gyration of 0.8 m. Its speed is 200 rpm. The ship pitches 5o above and below the mean position. A complete oscillation takes place in 20 s and the motion is simple harmonic. Determine i. the maximum couple tending to shear the holding down bolts of turbine, ii. the maximum acceleration of the ship during pitching, and iii. the effect of gyroscope, if the rotation of the rotor is clockwise, when looking from aft.