(b) A fragile instrument which comprises of two masses m1 = 50 kg and m2 = 200 kg is connected by a rigid massless horizontal rod of length, I=1 m as shown in Figure Q3. The masses are suspended by four identical springs, each with stiffness, k = 1000 N/m. Assume that the instrument behaves in coupling coordinate free vibration system; (i) Sketch the free body diagram of the system by including the location of center of gravity and values of l1 and l2. (ii) Derive the equations of motion of the system in matrix form [M]{x}+ [K]{x} = 0 by including all the values of m1, m2, l1 and l2. (iii) Find the natural frequencies and mode shapes of the system.

(b) A fragile instrument which comprises of two masses m1 = 50 kg and m2 = 200 kg is connected by a rigid massless horizontal rod of length, I=1 m as shown in Figure Q3. The masses are suspended by four identical springs, each with stiffness, k = 1000 N/m. Assume that the instrument behaves in coupling coordinate free vibration system; (i) Sketch the free body diagram of the system by including the location of center of gravity and values of l1 and l2. (ii) Derive the equations of motion of the system in matrix form [M]{x}+ [K]{x} = 0 by including all the values of m1, m2, l1 and l2. (iii) Find the natural frequencies and mode shapes of the system.

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

Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128
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?
Consider a simple model of an airplane wing given in figure below. The wing is approximated as vibrating back and forth in its plane and is massless compared to the missile carriage system (of mass m). The modulus and the moment of inertia of the wing are approximated by E and I, respectively, and / is the length of the wing. The wing is modeled as a simple cantilever for the purpose of estimating the vibration resulting from the release of the missile, which is approximated by the impulse function FO), Calculate the response and plot your results for the case of an aluminum wing 2-m long with m=1000 kg, z-0.01, and I-0.5 m'. Model F as 1000 N lasting for 10 s. Bp view At with miss (a) (b) Flay Simplified beam mdel Vilration modd Need detailed solutions for these question 8.png 4.png Submit th.
Q2 : (Section A) A engine valve assembly shown by figure. If J is the inertia caused by the right-hand side of the rocker arm. Derive an equation for the natural frequency of the rocker arm. Assume sin (0) = 0 and cos (0) = 1. pivot rocker arm m cylinder head valve spring combustion chamber pressure (a) (b) (Section B) A gun barrel of mass 500kg has a recoil spring of stiffness 3,00,000 N/m. If the barrel recoils 1.2 meters on firing. Determine: (a) Initial velocity of the barrel. (b) Critical damping coefficient of the dashpot which is engaged at the end of the recoil stroke. (c) Time required for the barrel to return to a position 50mm from the initial position.
A simplified SDOF model of a vehicle suspension system is shown in below Figure. The mass of the vehicle is 500 kg. The suspension spring has a stiffness of 100,000 N/m. The wheel is modeled as a spring placed in series with the suspension spring. When the vehicle is empty, its static deflection is measured as 5 cm. (a) Determine the equivalent stiffness of the wheel (b) Determine the equivalent stiffness of the spring combination. (c) Determine the natural frequency fn of the system ks kw m ww Suspension spring Wheel I stiffness
Figure below shows a rod with mass M = 100 kg, cross section area A = 10 cm². The rod is supported by 4 springs having stiffnesses of k = 1 MN/m. A tip mass with m = 120 kg is attached to the rod. Assume x is the degree of freedom of the equivalent system. The Young's modulus, E, is not known. If the natural frequency of the equivalent mass-spring system is 40 Hz, determine the Young's modulus, E. Assume the length of the rod is L = 5 m. Find the nearest answer. k ww E, A, M k F @www.ww wint L 195 GPa 179 GPa 116 GPa 45 GPa 236 GPa 000 00
Refer to Figure Q2. A tray of mass mı is supported by 3 springs as shown in Figure 3(a). The natural frequency fa is 5.0Hz. An additional mass motor of m2 = 3.0kg (in OFF condition) is placed at the center on top of the mass, the natural frequency is observed to be 2.5Hz. a) Calculate the mass mı. The motor m2 is ON and it rotates at the speed of 600 rpm. Calculate: a) The transmissibility b) Attenuation c) Explain what will happen if the system run at Resonant Frequency m2 m1 Figure 2(a): Original system Figure 2(b): system with m2 added
k, k3 A В k2 What is the equivalent spring stiffness between the points A and B. If ki = 1 N/m, k2 =1 N/m. k3 = 2 N/m and k4 = 2 N/m A N/m
Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C.Point A is connected to a spring to maintain the bar in vertical direction, and thestiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angleθ = 3.5 degree and released,(i) With the free body diagram and kinetic diagram, determine the initialhorizontal displacement of A. (ii) Determine the period of vibration. (iii) Determine the maximum velocity and acceleration at point A.
Question 10: Figure 4 shows a mechanical system. Mass m is attached at the end of the rigid rod, which has an inertia I about the pivot. Assume negligible pivot friction. The input is the displacement z. When z = 0 0 degrees, the spring is undeflected. Assuming a small 0, identify the equation of motion for with z as an input. m Figure 4: Mechanical System
The uniform bar shown in the attached figure is pivoted at point O. Its motion is controlled by three springs and a damper as illustrated; find the value of the damping coefficient C, if the damping ratio is to be 0.4. Given the following data Data: k₁-7000 N/m, k₂=8000 N/m, ky 10000 N/m, M = 12 kg, b=0.4 m a=0.2 m J-0.5 Kg.m² Lif ww Bar MJ $0 www.m
Parameters Mass 5kg A=2 B=7 C(m)=3 D(m)=4.583