QUESTION 1"A load of 8000N resulted in a static displacement of 0.2m in a composite structure. A harmonic force of amplitude600 N is found to cause a resonant amplitude of 0.375 m. Find the hysteretisis damping constant of the structure(2 decimal places), the energy dissipated per cycle at resonancefrequencyfrequencyJoules/cycle (0 decimal places), the steady state amplitude at 0.4 X the resonantm (3 decimal places), and the steady state amplitude at 4 X the resonantm (4 decimal places). "

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Answered: "A load of 8000N resulted in a static…

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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5. A load of 5000N resulted in a static displacement of 0.05 m in a composite structure. A harmonic force of amplitude 1000 N is found to cause a resonant amplitude of 0.1 m. Find (a) the hysteresis-damping constant of the structure, (b) the energy dissipated per cyde at resonance, (c) the steady-state amplitude at one-quarter of the resonant frequency, and (d) the steady-state amplitude at thrice the resonant frequency. A. B = 0.1, AW = 314.16- cycle X = 0.010161 m, X = 0.00125 m B. B = 1.1, AW = 314.16, X = 0.010161 m, X = 0.00125 m cycle C. B = 0.1, AW = 414.16- X0.110161 m, X = 0.00225 m cycle D. B = 1.1, AW = 414.16- -,X = 0.110161 m, X = 0.00225 m cycle
A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 10 times the instantaneous velocity. 1) Let x denote the downward displacement of the mass from its equilibrium position. [Note that x>0 when the mass is below the equilibrium position. ] Assume the mass is initially released from rest from a point 3 meters above the equilibrium position. Write the differential equation and the initial conditions for the function x(t) 2) Solve the initial value problem that you wrote above. 3)Find the exact time at which the mass passes through the equilibrium position for the first time heading downward. (Do not approximate.) 4)Find the exact time at which the mass reaches the lowest position. The "lowest position" means the largest value of x
4. A convenient way to measure damping in a single-degree-of-freedom system is called logarith- mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and t2 denote the times corresponding to two consecutive displacements ₁ and 2 measured one cycle apart, i.e., where t₂ = t₁ + T 2π Wd According to (4), show that the logarithmic decrement dis T = x1 8 = log = x2 where log has base e. Combine (5), (7), and (8) to obtain = (WnT 8 4π² +8² Will this method work for other initial conditions? why?
Question (2). The following system has a block of a mass m = xykg(from your registration mumber), stiffness k= 12000 N/m, damping coefficient c= xy• 10 kg/s, base motion y(t) = 0.01 sin(3t), calculate the following: %3D %3D 1. Natural frequency. 2 Base frequency. 3. Steady-state part of the response 4. Isolation range. X(t) m k Ay() base
Mass: 10 kg Can move up and down only k: 600000 N/m Fixed a) Find the 1“ 5 natural frequencies for above system K 600,000 m 10 f = -=38.9848hz b) If a force F = 200sin50t is applied at the top of the system, find the time response of the lowest point of the mass. Assume damping 6% of critical damping. c) For case b, do harmonic analysis and find the response of the lowest point with frequency for 0-100 hz. Can you solve only part B and part C.
2. The equation of motion for a damped multidegree of freedom system is given by Where [m] = [m]{x} + [c]{x} + [k]{x} = {f} [100 = 0 0 0 10 0 10. 1000-4 {f} [c] 8 –4 0 8 – 4 -4 4 0 8 4 = 100 2 0 = Focos(wt) -2 -2 The value of Fo 50N and w 50 rad/sec. Assuming the initial conditions to be zero and using the modal coordinate approach, find out the steady state solution of the system in the modal coordinate for first mode. Plot the steady state solution using the computational tools. 0 −2], [k] = = 2
PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = 6000 kN/m. d) Derive the equations of motion. e) Find the natural frequencies and mode shapes of the system. f) Find the free-vibration response of the system for the initial conditions: v(0)= {1} cm cm, v (0) = m Sec 00000 m k 00000 k x₁ (1) Jour 5k 0000 m Figure 3 00000 m 00000 k k x₂(1) - X3 (1) ܠܠܠܠܠܠܠܝ
For the system shown in Figure 2, u (t) and y (t) denote the absolute displacements of Building A and Building B, respectively. The two buildings are connected using a linear viscous damper with damping coefficient c. Due to construction activity, the floor mass of Building B was estimated that vibrates with harmonic displacement that is described by the following function: y(t) = y,cos (wt). k/2 Building A H k/2 M(t) C 73(1) Building B Equivalent (Building A) 00000000 Figure 2: Single-degree-of-freedom system in Problem 2. 111 uft) Please compute the following related to Building A: (a) Derive the equation of motion of the mass m. (b) Find the expression of the amplitude of the steady-state displacement of the mass m. (1) (Building B)
5. A load of 5000 N resulted in a static displacement of 0.05 m in a composite structure. A harmonic force of amplitude 1000 N is found to cause a resonant amplitude of 0.1 m. Find (a) the hysteresis-damping constant of the structure, (b) the energy dissipated per cycle at resonance, (c) the steady-state amplitude at one-quarter of the resonant frequency, and (d) the steady-state amplitude at thrice the resonant frequency. A. B = 0.1, AW = 314.16- cycle ,X = 0.010161 m, X = 0.00125 m B. B = 1.1, AW = 314.16- cycle ,X = 0.010161 m, X = 0.00125 m C. B = 0.1, AW = 414.16. cycle ,X = 0.110161 m, X = 0.00225 m D. B = 1.1, AW = 414.16- сycle -,X = 0.110161 m, X = 0.00225 m
A N6lb weight is attached to a spring with natural length sA. With the attached, the spring measures 8aft. The wright is imitially displaced 3ft bebw equilibrium and given an upward velocity of aftls. The medium resists the motion w/ force of one Ib for each ftlsec of velocity. lwhatis the natural frequency of the mass and spring in herts? )What is the critical damping coefficient in 1b-sec/? secends will the mass cross the equilibrium for the 2)Afer how many nd time? 3 4) What is the dam ping condition?
Question (2). The following system has a block of a mass m = xykg(from your registration mUrnber), stiffness k= 12000 N/m, damping coefficient c = xy• 10 kg/s, base motion y(t)= 0.01 sin(3t), calculate the following: %3D 1 Natural frequency. 2 Base frequency. 3. Steady-state part of the response X(t) k y(1) base wW
Consider the following for a single-degree-of-freedom system with m = 1. X, k = 2.5, and c = 1.8. Here, the value of X indicating of the number of your group. For example, if your group number is 15 gives X = 15, therefore the values of m = 1.15. If your group number is 9 gives X = 9, therefore the values of m = 1.9 Find; (i) Natural frequency, Wn (ii) Linear frequency, fn (iii) Critical damping constant, cc (iv) Damping ratio, 3 (v) Damped frequency, wa

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