A disk of mass, m, and radius, R as shown in thefigure is being supported by an elastic shaft with adiameter, D, and length, L. Use G as the shearmodulus of the elastic shaft. A linear damper witha damping coefficient c is used as a model fordamper of a disk that can oscillate about itsvertical axis. Provide an expression of the motionof a disk. RGDm1

Answered: Image /qna-images/answer/46016286-1a5f-44b6-b79d-5395b0db4549.jpg

Answered: A disk of mass, m, and radius, R as…

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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Consider the system in Figure 1-a, which is initially at equilibrium. The massless bar AOB with point mass m = 2 kg attached to B rotates with rotational viscous damping coefficient b about the fixed point system is connected by a horizontal spring (acting at B) to a fixed wall. The rotating bar has a length 3L=1.5 meters. L 2L k twine ww Figure 1-a A Rotational viscous damping coefficient b B g Massless a) Write the linearized equation of motion of the system (Figure 1-a) for small angular displacement 0 (t). (Symbolic)
Problem 2. For the single-degree-of-freedom mechanical system shown in the figure, the bar has mass m and length l (so that Io spring is unstretched when 0 = 0: ml² 피). If the %3D k a) find the linearized governing equations of motion for small 0; (т,1) b) find the natural frequency, damping ration, and damped natural frequency of oscillation for the free response; Neglect gravity.
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k 0.5m- 1m The moveable mass is removed, the spring stiffness increased to k= 500 N/m and a viscous damper is added to the system. The new system is show in the figure above. The mass of the slender rod remains 6 kg. For what value of the damping coefficient C will the system be critically damped? (round your answer to the nearest whole number) A Ns/m
Question
As illustrated in the figure below, the bedplate of an experimental diesel engine is supported on four springs to isolate the vibrations from the test frame. The effective weight of the diesel engine and bedplate is 43kg and the stiffness of each of the four springs is 250 kN/m. Using a simplified approach - by applying Newton's Second Law assuming a single degree of freedom system and ignoring damping - what rotational engine speed is best avoided? Bedplate Test engine Supporting springs Figure: Sketch of a test engine mounting arrangement Give your answer in rad/s to 1 decimal place.
Suppose that a horizontal string of length c =2 with fixed end points (the end points are fixed on the horizontal axis) is initially raised at its mid point to the height h above the horizontal and then released (no initial velocity). Write the boundary value problem modeling the vibrations of the string and solve the problem.
In this lab, we will observe the free response of a first order mechanical system: a rotating bicycle wheel. As shown in the figure, suppose that the bicycle wheel is suspended above the ground, and is free to rotate on its axle. Assume that the only source of damping is the axle bearing, and that after time t=0 no external torques act on the wheel. ✈0(1) a) Derive the differential equation describing the angu- lar velocity of the wheel (t), in terms of the moment of inertia J and the damping B. b) Assume that a time t= 0 the wheel has initial an- gular velocity 22o. Solve the differential equation for response (1). c) Normally, we plot the response as (t) versus t. In- stead, suppose we plot the response as log, (n(t)/Ng) versus t. What type of curve is this plot? If you mea- sured experimentally logg ((t)/no) as a function of t, could you determine the system time constant 7 from the curve? d) What is the time constant 7 of the system expressed in terms of the moment of inertia J and…
Statement of question: A centrifugal pump having a mass of m1, having an unbalance of me, is supported on a rigid foundation of mass m2 through isolator springs of stiffness k1 as shown in Figure Q1. The centrifugal pump on a rigid foundation can be modeled for vibration analysis in the x direction as Two-degree-of-freedom system. The mass of the pump m, and the foundation, m2 can be approximated as 360 kg and 900 kg respectively. Whereas, the the soil stiffness k2 is 175 kN/m. The soil damping c1 is 35 kN.s/m. The mass m and eccentricity e of umbalence are 0.23 kg and and 0.15 m respectively. Discuss the system response for the pump speed of 1200 rpm using modal analysis for isolator spring stiffness of 300 kN, 350 kN and 400 kN. The total vertical component of the exciting force on the centrifugal pump is given by F(t) = mew² sin wt. F(t) = mew sin wt Centrifugal pump (mass, m1) m1 Isolator springs (stiffness, k1) Foundation m2 (mass, m2) k2 Soil (stiffness, k; damping, c2) A…
A spring-mass-damper system has mass of 100 kg, stiffness of 3000 N/m and damping coefficient of 300 kg/s. Calculate the undamped natural frequency, the damping ratio and the damped natural frequency.

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