A. Find the equations of motion for the system shown in the figure. Express the equations using thestate variables theta and thetadot, which correspond to the angle of bar AB relative to the verticaland its angular velocity. You may approximate small displacements.B. Derive an expression for the natural frequency of the system.b10x2Bm1x1k₁m2k2www(Ctrl)

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Answered: A. Find the equations of motion for the…

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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2. The mechanism presented in the figure is programmed to produce an oscillatory motion defined by theta-theta_0*sin(w0*t). Find the amplitude of the velocity and angular acceleration.
solve please by lagrang method to find the eqation of motion and to find the frequencies and mode, please indetail. a : 255 mm b : 100 mm L : 400 mm M : 1.1 kg m : 0.995 kg k : 5 N/mm
How do you read this text and understand what number goes where?
rad The rod OA rotates clockwise at a constant angular velocity of 0 = (3) Two pin-connected slider block, located at B, move freely on OA. The curved rod is described by the equation r (300 (3-cos)) m. Hint: 1. Remember clockwise rotation is negative velocity. OA Variable 0₁ d₁ d₂ d3 0₁ d2 d3 Values for the figure are given in the following table. Note the figure may not be to scale. Value 110 degrees 0.45 m 0.1 m 0.275 m Using cylindrical components, a. Determine the cylinders's radial and transverse components of velocity at the instant shown, u, and vg. b. Determine the cylinders's radial and transverse components of acceleration at the instant shown, ar and ag. c. Determine the cylinder's magnitude of the velocity at the instant shown, ·M. d. Determine the cylinder's magnitude of the acceleration at the instant shown, |a1. Round your final answers to 3 significant digits/figures. 7= fr + a= M-C Hr+ m S M 82 He) Fe) m S m
Crack AB of a slider crack mechanism shown in Figure 2 rotate at a constant speed of 300 rpm in clockwise direction. The connecting rod BC has a length of 1 m and incline at 45° to vertically positioned piston C. B 1m A 0.2 m 457 C Figure 2: Slider crank mechanism Draw the displacement diagram of the mechanism shown in Figure 2 to scale. Use a vector diagram to determine the velocity of the piston C and connecting rod BC. Calculate the acceleration of piston C and the angular acceleration of connecting rod BC.
The following mass-and-spring system has stiffness matrix K. For the mks values, find the two natural frequencies of the system and describe its two natural modes of oscillation. k₁ k₂ K3 K= - (K₁ + K₂) k₂ m₁ = 1, m₂ = 5; k₁ = 3, k₂ = 15, k3 = 15 k₂ - (K₂ + K3) Describe the mode of oscillation for w₂. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The two masses move linearly, staying a fixed distance apart. B. The two masses oscillate in the same direction, where the amplitude of m₁ is O C. The two masses oscillate in opposite directions, where the amplitude of m₁ is D. The two masses oscillate in the same direction with equal amplitudes. E. The two masses oscillate in opposite directions with equal amplitudes. times the amplitude of m2. times the amplitude of m₂.
منه Ri سے b (1) Starting with the position equation R=Ay, where A is the rotation malux about the 7 oxis and u is a point on the position Vector, derive the velocity equations in both algebraic and matrix foven to solve for Ws and bi What are the vector position and velocity equations? Your motorx equatons must be in the forem: [ ] [ 11 ] = [] [][ b (2) From part 1 device the matrix equation to solve for us and b Wz B = [ w₁] = [ ][ ] b ୧ (3) with the values R₂ = 2in, Rs = 101, R₁ = 8in, Ə₂ = 40°, s = 185' and W₂ = 10 rad/sec B = = [w] Don't forget units Solve w₂ and b. ☐☐ い

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Question 1 A sketch of a valve and rocker arm system for an internal combustion engine is give in below figure. Model the system as a pendulum attached to a spring and a mass. Determine the equations of motion and calculate the natural frequency in rad/s. The mass moment of inertia of the rocker arm about its pivot point j=0.46, the stiffness of the valve springspring k=420 , the distance from pivot to spring I= 0.98 m, and the mass of the valve m=3.2 kg. Ignore the mass of the spring and the oil effect. Rocker arm Follower k Valve spring LOil Cam m Valve

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