Show this complete solution for this force driven without damping equation: Consider a driven undamped spring/mass systemdescribed by the initial-value problemd²x+ w²x = Fosin" yt, x(0) = 0, x'(0) = 0.di²(a) For n = 2, discuss why there is a single frequencyY₁/27 at which the system is in pure resonance.(b) For n = 3, discuss why there are two frequenciesY₁/27 and y2/2π at which the system is in pureresonance.(c) Suppose w = 1 and Fo= 1. Use a numerical solverto obtain the graph of the solution of the initial-valueproblem for n = 2 and y = y₁ in part (a). Obtain thegraph of the solution of the initial-value problem forn = 3 corresponding, in turn, to y = y₁ and y = y2in part (b).

Solution: Given Data: d2xdt2+ω2x=Fosinnγtx0=0dx0dt=0 To Find:

Answered: Consider a driven undamped spring/mass…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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7. The figure below shows a single degree of freedom control surface/actuator system. The control surface has a mass moment of inertia /= 30 kg.m² about the hinge, the effective actuator stiffness and damping values are k = 3000 N/m and c= 500 Ns/m respectively and the rotation of the control surface is 0 rad. The actuator lever arm has length a = 0.2 m. A force f(t) = 58(t) N is applied to the control surface at a distance d = 1 m from the hinge. It is assumed that the main surface of the wing is fixed rigidly as shown in the figure. Assume small angle approximation. Determine the tip velocity (velocity at the location of f(t)) at t = 0.1 s 0 (t) f(t) a I Quinn. a) 285.64 mm/s b) 152.74 mm/s c) 499.47 mm/s d) 400.63 mm/s e) 583.77 mm/s d
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A uniform rod of mass m is pivoted at a point O as shown in Figure 2. The rod is constrained by three identical linear springs, and a point mass M is attached at the end of the rod (also shown in Figure 2). The parameters of the system are as follows: L= 1 m, k = 1000 N/m, m= 50 kg, M = 25 kg. i. Derive the equation of motion of the system in terms of the angular displacement (0). Choose O as the clockwise angular displacement of the rod from the system's static equilibrium position.
The torsional system of Figure Q6 oscillates about the centre of the disc. A linear spring and a linear damper are attached to the disc at radius r. A linear damping element is also attached at the edge of the disc at radius R. For this system assume that r = 0.15 m, R = 0.25 m, mass of disc m = 5 kg, stiffness coefficient k = 1200 N/m, and damping coefficient c = 10 Ns/m. Set up the differential equation of motion for this mechanical system. k Fin с R Figure Q6 C Disc 0
Two identical thin bars, each of mass m and length L, are welded together at a right angle as shown in figure 1. This T-shaped assembly is pinned to ground at point 0. Block B is given a prescribed forced displacement xg = b sin øt. Friction and damping are neglected. a) Derive the equation of motion for the system in terms of the angular position of the bars, 6, and parameters m, L, k, and g; b) Derive an expression for the natural frequency of the system; c) Derive an expression for the forced angular response of the system; L/2 L/2 L Хв
A pulley 610 mm diameter is driven at 300 revs/min by a belt, the tensions in the tight and slack sides of the belt being 670 N and 270 N. Find the power transmitted.
Problem 11
In the figure, a rigid rod of mass m is supported by a spring with rotational stiffness kR on the left and a vertical displacement stiffness of 1.5k on the right. Calculate the system's equation of motion and the natural vibrational frequency. (Assume the angle of rotation is small.)
Consider a mas5--spring system governed by the second order differential equation of the form nn" +n' + ky = f(1) i) Explain the significance of each and every term in the given equation. ii) Assume thał m = 1, r = 6, k = 9, f(1)= cos 31 and y(0) = y'(0) = 0 . Find the motion of %3D the system using method of undermined coefficients. Explain the result. 1ii) What kind of solution do you expect for the given problem if r = 0 , Discuss the solution.
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