QUESTION 3A machine tool, having a mass of m = 1000 kg and a mass of inertia of Jo = 300 kg.m², issupported on elastic supports, as shown in Figure Q2. If the stiffnesses of the supports are givenby kl = 3000 N/mm and k2 = 2000 N/ mm, and the supports are located at 11 = 0,5 m and 12 =0,8 m, determine the natural frequencies and mode shapes of the machine tool. Develop thestate-space model. Use numerical integration to compute and plot the time response of thesystem (newtons) subject to your own initial conditions.m, kFigure Q3

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Answered: A machine tool, having a mass of m 1000…

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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Please solve this problem by showing the manual calculation and choose the correct answer(SUBJECT: mechanical vibrations)
Seen in Figure 1, a rotating mass (with mass moment of inertia Id to a fixed wall (on the far left) by a torsional spring (k 1kg* m² and angular position a) is attached 1Nm/rad) and a torsional damper. Consider the spring and damper as concentric and in parallel. Dampers with damping ratios of c = be considered. Att = 0.1, 0.5, 1.0, and 1.5kg * m²/s will 0, a unit step torque Tin is applied to the rotating mass. A unit step input is a forcing function whose value is 0 from -∞o to some time to and 1 from to to oo. Here, to = 0. Your tasks: k ww + C = la Od A Derive the equation of motion of the rotating mass. Write c as EOM's for the different values of c. Tin 0 Figure 1: Schematic of the mechanical system to model in Problem 1. em, you will solve part B over MA AB Grader Plea LO onment variable. You do not need to write separate ד ו. for
B/ Two massless springs with spring constants k1=100 and k2=150 are attached to mass of (m=20 kg) at A in parallel as shown in Fig (a). An identical pair of springs is attached to mass B in series as shown in Fig (b). Taking mA = mB = m, find and compare the natural frequencies ws and wp and (ws/wp) of the two systems. (b)
The 20-lb rectangular plate has a natural period of vibration t = 0.4 s, as it oscillates AB. Neglect the mass of the rod. Suppose that a = 2 ft, around the axis of rod b= 4 ft. (Figure 1) Figure k b 1 of 1 Part A Determine the torsional stiffness k of the rod, measured in lb. ft/rad. Express your answer in pound-feet per radian to three significant figures. ΑΣΦ ↓↑ vec k = Submit U Provide Feedback Request Answer ? lb ft/rad
Pls see question in the attached image and solve the question by hand written notes and figure.
7. The arrangement in the drawing shows a block (mass = 14.0 kg) that is held in position on a frictionless incline by a cord (length = 0.582 m). The mass per unit length of the cord is 1.30 x 10-2 kg/m, so the mass of the cord is negligible compared to the mass of the block. The cord is being vibrated at a frequency of 166 Hz (vibration source not shown in the drawing). What is the smallest angle 0 between 15.0° and 90.0° at which a standing wave exists on the cord?
Vibration
III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.
igure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y 0, and the springs are in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. DE only 225 Your tasks: X k 0 3k a F a M y A Derive an equation of motion for the system in terms of the angular displacement 0, and its derivatives (you should not have y or its derivatives in this equation.) B Derive an equation of motion for the system in terms of the displacement y, and its derivatives (you should not have or its derivatives in this equation. C Assuming there is no external actuator force F acting on the system, write down the total energy H of the system in terms of 0,0 and element constants. Derive an expression for the time derivative H of the total energy. D Transform the equation from part B, which is in y, to another…
answer ASAP would be appreciated
Figure below shows an aircraft fighter. The wing of the aircraft may be modelled as a clamped wing with two lump masses at its centre and tip. The two masses represent the mass of the wing and the missiles. The equivalent model shown in the figure is used to estimate the first two natural frequencies of the wing and therefore the fuselage can be assumed rigid. 24EI If m1 = am, m2 = bm and bending stiffnesses of the beams are k where a = 9.7147 and b = 4.1873 and if w, and wz are the first and second natural frequencies of the system, w2/wz is: x, (t) x2(t) EI т, EI (m2) /2 1/2 3.2719 2.4236 1.3088 1.7692 4.7260

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