B7 Please help on the attached question. Q7. For the system shown in Figure 3 where a vertical mass m is connected to the midpoint of theslender bar of mass m and length L through a spring of stiffness k. Denote the displacement of thevertical mass by x and the small rotational angle of the slender bar by 0. Find the free vibration0(t)x(t)responseof the system with the following initial conditions: x(0) = 0, 0(0) = 0,x(0) = 2m/s,ė(0) = 0. Given: m = 2 kg, L = 1m, k = 1KN/m, the natural frequencies have beencalculated to be w₁ = 16.69 rad/sec, w₂ = 36.69 rad/sec, the associate mode shapes are found to be1-0.294911.128=MTXТоslender bar

Answered: Q7. For the system shown in Figure 3…

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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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.
100 As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the spring constant at time t is k(t) = t sin N/m. If the mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is subjected to the harmonic external force f(t) = 100 cos 3t N. Find at least the first four nonzero terms in a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement: Analytically (hand calculations)
Consider the double mass/double spring system shown below. - click to expand. Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity). We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are -0.039-0.248i 0.813 A₁2=-0.5±3.2i, v₁ = 0.024 +0.153i -0.502 -0.134-0.302i 0.409 -0.2160.489 0.661 (a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero. A3,4 -0.5± 1.13i, z = and (2₁ (0), ₂(0)) = Enter your answer using angle braces, (and). (b) At what frequency will the masses be oscillating in this mode? Frequency rad/s
6. A weight of mass M = 8 kg is suspended by a spring with k = 10 N/ m and c = 1.6 N s/m. Determine the general vibration response to this homogeneous system by converting the equation to a state-space equation and solving it using eigenvalues and eigenvectors.
The motion of a spring-mass-damper system satisfies the initial value problem: d²x m- +bd + kx = F, x(0) = 0; *(0) =1 di? dt Given m = 1 kg, b= 5 Ns/m, k = 4 N/m, and F = 5 N. (a). What is the natural frequency of the system? (b). Is this system under damping or critical damping or over damping? Explain it. (c). Solve the given initial value problem. (d). The location of poles of X(s) affects the behavior of the system. How to choose parameters b/m and k/m so that the poles are placed at - 4+4j?
100 As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement: • Analytically (hand calculations) Creating Simulink Model Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph for the first 15 sec. The graph must be fully formatted by code.
Whats the first equation (circled) and how did we get it ?
3. A washing machine of mass 70kg operates at 1600 rpm. Find the maximum stiffness of an isolator that provides 80 percent isolation. Assume that the damping ratio of the isolator is 5 percent
Please find the question attached.
1
This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c= 80 N-s/m The ball is started in motion with initial position to 9 m and initial velocity vo = -48 m/s. Determine the position function z(t) in meters. r(t) = Graph the function z(t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co, wo and co S 38 E Co= Wo= (assume 0 do < 2π) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping. α0 =
Q.2 Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shown below. Write the equation of motion of the system using D'Alemberts principle. Find the natural frequency of vibration of the system. J6+ (kde) ds. C 0000 m

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