Question 4A light aircraft nose landing gear is to be simply modelled as masses and springsillustrated in Fig. 3. The stiffness and mass of the tyre is given by k2 and m2respectfully. The stiffness of the landing gear is given by kl and the mass of the aircraftby mi. There is no damping and it is only free to vibrate in the vertical direction. Writethe equation of motion for this system in matrix form.Calculate the natural frequencies if the following values are given kı=10* N/m, k:=10³N/m, mi-2000kg and m2 = 50kg.c) Determine the modal matrix to solve this problem.Fig. 3 Nose landing gear and ModelXIX2kık₂mim2

Answered: Image /qna-images/answer/decfc274-6bd0-460b-9efe-421907f43df3.jpg

Answered: * A light aircraft nose landing gear is…

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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Damped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k b
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?
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
For the shown spring-mass-damper system. Let m =1 kg, b = 2 N.s/m, k = 2 N/m and f(t) = sin2t N. (a) Write the equation of motion. (b) Find the amplitude of the steady state oscillations. (c) Find the steady state maximum acceleration.
6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support
Question 4For the dynamic system shown in the figure,derive the equations of motion using Lagrange’s equations.
2. A kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. (b) Find the solution to your initial-value problem from part (a). (c) Graph the solution found in (b) on (0
Problem 5 Consider the two-mass system connected by two springs. Let coordinates x, and x, be such that when they are both zero, the springs are at their natural lengths. Write down the equations of motion. Use the Matlab command ode45 to solve the initial value problem with parameters m = m2 = k, = 1, k2 = 10 and initial conditions x,(t = 0) = *,(t = 0) = *,(t = 0) = 0, x2(t = 0) = 0.1 for te [0,67]. Plot x, and x2 as functions of t. Submit your plot as well as codes.
Question 9: Figure 3 shows a mechanical system. The rod (with moment of inertia J) rotates about the pivot at only small rotation angles. As pictured, theta is positive clockwise. Attached is mass m, which moves positive to the right. When stationary in the position shown, all springs are undeflected. Using BOBODDY, find the mathematical model of this system assuming small rotation angle 0. Link, moment of inertia J k3 L₁ 12 5 Ꮎ wwww Figure 3: Mechanical System m k₂ b
Consider the system shown below. Answer Questions 6-11 based on this figure. How many degrees-of-freedom does the system shown below has? The two pulleys have the identical mass, radius, and the moment of inertia. т, 1, R k т, 1, R Variables x: vertical position of the moving pulley 8: rotation of the moving pulley p: rotation of the fixed pulley m: pulley mass R: pulley radius I: mass moment of the pulley about its own center of mass. k: spring stiffness T: cable tension Assumptions 1. x = 0, 0 = 0, and o = 0 when the spring is undeformed. 2. The cables and springs have negligible mass. 3. There is no slip between the pulley and the cable. 4. Only two-dimensional planar motion is allowed.
For the problem related to Fundamental.4, a sketch of the considered system showing and naming (or numbering) every part of the system considered, the respective velocity and acceleration of each, and the frame of reference considered is mandatory. Its absence will automatically make the problem false. Gear A on the drive shaft of the outboard motor has a radius rA=3 in. and the meshed pinion gear B on the propeller shaft has a radius rB=64 in. The point P is located on the propeller's tip at a distance 7 in. from the neutral axis of the propeller's shaft. P B At the beginning of the propulsion, the drive shaft rotates with an angular acceleration a = A. t2.2 rad.s2 where t is in seconds. what must be the value of A to have, while starting from rest, vp=21 in.s1 in 5 seconds ?
For the mechanical system shown below, find the equation of motions and the system matrix. Where (x = X ewt)

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