A single degree-of-freedom linear elastic structure was subjected to a series of harmonicexcitations, one at a time. The excitations had the same forcing magnitude but different forcingfrequency. Forcing frequencies and observed peak steady-state displacements are shown in the graphbelow. Find the natural period and damping ratio of the structure.Displacement (mm)6050403020100012.34Forcing frequency, f [Hz]54.67

Answered: Image /qna-images/answer/faeb520e-506f-4077-a04d-1a03233b5e97.jpg

Answered: A single degree-of-freedom linear…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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A 19 kg object is attached to a spring with spring constant 16 kg/s2. It is also attached to a dashpot with damping constant c = object is initially displaced 5 m above equilibrium and released. Find its displacement and time-varying amplitude for t > 0. 7 N-sec/m. The y(t) e-0.184t (5 cos (0.9t) + sin(0.9t)) The motion in this example is O critically damped O overdamped O underdamped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t) 4 cos(wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? 0.977 What is the maximum possible amplitude? 2.30
A mass of 7.9 kg oscillates at the end of a spring of stiffness 26.1 Nm-¹. If the damping ratio is 0.2, determine the damped natural frequency in rad/s. (Express answers to 2dp) Answer:
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t. Design the following application case The mechanical vibration system is shown in Figure (a). When a step input with 3N amplitude is subjected to this system, the movement rule of the mass m is shown in Figure (b). Evaluate the values of mass m, damping constant c and spring constant k. m (a) F-3N XX 1.0 x(1)(cm) 0 2 (b) M,-0.095 Ⓒ
Please do #11 section 3.6
Use Buckingham Pie Theory to establish the design conditions. A machine weighing 6,300 N is mounted on 10 springs each having a modulus of 105 KN/m. At intervals of 8s, it is subjected to a repeated vertical force having amplitude of 1,400 N and varying as one loop of a sine-curve with duration of 0.20 s. It is desired to study the vibration characteristic using a true model having a length scale of 12. Establish the design conditions, assuming that the vibration is restricted to only the vertical displacement.
For a single degree of system mass is 20kg stiffness=6.25kN/m damping coefficient 20Ns/m.Initial displacement at t=0 is zero and initial velocity is 150m/s obtain the equation of motion and find the displacement at 2seconds
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4 Assume that there's no damping. Please indicate if the system exhibits resonance.
A mass of 10kg oscillates at the end of a spring of stiffness, 5N/m. If the damping in the system is such that it gives a damping ratio of 0.45, determine. i) The critical damping. ii) The value of the damping coefficient. iii) The damped natural frequency. iv) The equation for the displacement if the initial velocity is 0.025m/s, and the initial displacement is 0 m.
A concrete part with a mass of 800 kg is hung on a 6 m long steel cable. You determine the spring constant to be 3.924 \times 10 ^ 6 N/m. What is the oscillation period when the steel beam oscillates in the direction of the cable? Provide the result in seconds.

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