A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as illustrated in the figure below (note figure is not drawn to scale). The beam is supported by two springs of stiffness, k₁ and k2, located at a distance, L and a respectively, from the pivot. Additionally a damper with damping coefficient cis located a distance b from the pivot. A step force of constant magnitude, F(t) = Fo is applied to the mass from time t = 0 as illustrated. Using the data below, derive the equation of motion of the system. m = 15.6kg; a=0.5m; b=0.8m; r = 0.62m; L = 1.25m; k₁ = 772Nm¹;k2 = 340Nm¹; c= 95Ns/m; Fo= 86N Determine the moment of inertia of the system, Io, about point O.

A mass, m, is supported on a light beam, which is free to rotate about the pivot at O as illustrated in the figure below (note figure is not drawn to scale). The beam is supported by two springs of stiffness, k₁ and k2, located at a distance, L and a respectively, from the pivot. Additionally a damper with damping coefficient cis located a distance b from the pivot. A step force of constant magnitude, F(t) = Fo is applied to the mass from time t = 0 as illustrated. Using the data below, derive the equation of motion of the system. m = 15.6kg; a=0.5m; b=0.8m; r = 0.62m; L = 1.25m; k₁ = 772Nm¹;k2 = 340Nm¹; c= 95Ns/m; Fo= 86N Determine the moment of inertia of the system, Io, about point O.

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

Figure 2 shows an electrical motor with mass M=13 kg located at the middle of pinned-pinned beam. A damper with damping coefficient of c=59 N.s/m is also attached to the beam at point A . Considering Young’s modulus of the beam E=98 GPa, moment of inertia of the beam I=18 mm4, length of the beam L=1 m, unbalance mass of m0 =1.9 kg, eccentricity e=2.8 mm, and zero initial conditions, find the steady state amplitude of point A at resonance in millimetre (mm).
1: the mass damper spring given in the figure on the side is a harmonicit's under the influence of force. a-) obtain the equation of motion by making the necessary admissions for this system. B - ) natural frequency of the system using the values given in the table, damping State (critical, etc. ), find and interpret the damping constant and degrees of damping. c-) t = 5s with t = 20s compare the situation in their time. What changes have occurred?
The door of a house has a height of 2 m, the width of 1 m, the thickness of 50 mm and mass of 50 kg. The door opens against a torsion spring and a viscous damper as shown in the figure. If the spring constant of the torsion spring is kq = 15 N-m/rad, find the damping constant necessary to provide critical damping in the return swing of the door.?
In the system in the figure, the static equilibrium position of the thin, slender homogeneous rod of mass m and length L is horizontal.During the movement of the system, the bar is separated from the horizontal by small angles. (A makes oscillating motion with small angles relative to the simple support point)a) Find the equation of motion of the system in terms of the given parameters.b) Since M=4 kg, m=1 kg, L=1 m, k=600 N/m, c=200 Ns/m, F=300 N, w=4 rad/s, is there resonance in the system? If there is resonance, what would you recommend to get rid of resonance?
In the figure, a rigid rod of mass m is supported by a spring with rotational stiffness kR on the left and a vertical displacement stiffness of 1.5k on the right. Calculate the system's equation of motion and the natural vibrational frequency. (Assume the angle of rotation is small.)
A wooden plank of mass M is placed on the top of two identical, homogeneous cylinders, each of mass m. The plank is attached to a verti-cal wall with a horizontal ideal spring of stiffness k (see figure). Find the period of small oscillations of the plank. Assume that the coefficient of static friction is large enough so the cylinders don’t slip neither on the horizontal surface nor on the plank.
Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency. d) When x (0) = 0.01 m is pulled down at t-0 and when x (0) = 0 m / s is released, its movement x (t) is m = 3 kg, b-12 N / m / s and Find it using the values of k = 120 N / m. e) Find the transfer function of the system when there is a force input of F = 10 N downward (in the + x direction) to the object. f) Show this transfer function with a block diagram.
Figure below shows a body of mass m attached to a spring of stiffness k. Find the differential equation for the displacement, x
In the mechanical system in the figure, a rigid rod is bedded at point P and has mass m at its end. can rotate vertically. At the other end of the rod, a spring (k) and a damper (c) are attached. Draw the Free-Body Diagram of the system, obtain the Equation of Motion (the vertical position of the ball We assume that the displacement x is very small and the bar is massless).
Mechanical Vibrations Problem: A cylinder of mass m and mass moment of inertia J0 is free to roll without slipping but is restrained by two springs of stiffnesses k1 and k2, as shown in the figure. a) Find its natural frequency of vibration. b) Find the value of a that maximizes the natural frequency of vibration.
PART OF MECHANICAL VIBRATIONS SUBJECT USE VIRTUAL WORK The uniform bar shown in Fig. P3.6 has mass m, length l, and mass moment of inertia 1 about its mass center. The bar is supported by two springs kı and k2, as shown in the figure. Obtain the differential equation of motion and determine the natural frequency of the system in the case of small oscillations.
(machine dynamic ) The mass(20 kg)-damper-spring system given in the figure on the right is under a harmonic force. a- Obtain the equation of motion by making the necessary assumptions for this system.b- Find and interpret the natural frequency, damping state (critical etc.), damping constant and damping degrees of the system using the values given in the table.c- Compare the situation at t=5s and t=20s. What changes have occurred?