Free Vibration Acceleration Time History0.51,-0.424 secAccel, 0.423 g0.40.3t4.958 secAccel0.194 g020.1-0.1--0.2-0.3-0.4--0.5Time (sec)Calculate the natural frequency of the structurefrom the experimental testing results shownbelow which were obtained from a freevibration test of the SDOF structure.Acceleration (

Given: To find: natural frequency

Answered: Free Vibration Acceleration Time…

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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Example of Vibration System Analysis. Include appropriate model and complete label for mass, damping and spring elements.
The natural frequency ω of vibration of a mass M attachedto a rod, as in Fig. depends only on M and the stiffness EI and length L of the rod. Tests with a2-kg mass attached to a 1040 carbon steel rod of diameter12 mm and length 40 cm reveal a natural frequency of 0.9 Hz.Use these data to predict the natural frequency of a 1-kgmass attached to a 2024 aluminum alloy rod of the samesize.
The crankshaft-flywheel assembly of a large engine may be considered a torsion pendulum. The shaft is 1.8m long and transmit 179.127kN-m torque corresponding to 83MPa stress. The flywheel diameter is 75cm and weighs 4.5kN. If the modulus of rigidity of the shaft material is 77GPa, compute the period of vibration of this system.
The period T of vibration of a beam is a function of itslength L , area moment of inertia I , modulus of elasticity E ,density ρ , and Poisson’s ratio σ . Rewrite this relation indimensionless form. What further reduction can we makeif E and I can occur only in the product form EI ? Hint:Take L , ρ , and E as repeating variables.
A coffee table has a rigid top of mass 17 kg mounted on legs of total stiffness 38 MN/m and a damping coefficient of 1.6 kN/m/s. The coffee table is subjected to a vibrating force of 100 N. caused by sound waves from a nearby loudspeaker. Find the resonant frequency of the table, suggest a method to avoid the resonance for this table. Please provide a detailed solution. Thanks!!!
(Q4) A thermopile 18 constructed with Iron-constantan materials. Four junctions are maintained at 300°C and for junctions are maintained at 40°C. The output of the thermopile is connected to a potentiometer. What voltage will be indicated if both terminals of the potentiometer are at the same temperature? What is the temperature indicated in this case?
A steel beam (E = 30*10^3 ksi) and an aluminum (E = 10*10^3 ksi) beam are attached to an instrumentation box as shown. Both beams have a thickness of 0.30 inches and a width into the plane of the paper of 1.5 inches. Vibration measurements from the instrumentation box indicate a sinusoidal displacement with a maximum displacement max = 0.20 inches and a minimum displacement min = -0.2 inches. The stress concentration at both fixed supports is negligible. If AlSI cold rolled 1030 steel (Sut =76 ksi) is used, will the steel beam have an infinite fatigue life? (ignore instrumentation box length)
A closely coild spring of 20 cm mean diameter is having 25 coils of 2 cm diameter modulus of rigidity of the material is 10^7 N/cm^2. What is the stiffness of the spring?
A hard-drawn steel wire extension spring has a wire diameter of 4mm, an outside coil diameter of 28 mm, and initial tension of 1200 N is applied to the spring. The spring shows an extension of 85 mm. The approximate number of turns is 25. From the given information: Determine the physical parameters of the spring such as mean diameter, spring index, maximum shear stress, total number of turns, Wahl’s stress factor, free length of the spring, and pitch of the coil
What is the significance of analysis assumption in problem solving? LIke for mechanical vibration specifically damping element
A support beam used in one of the designs for the theme park, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations: x_1=3.75 sin⁡(100πt+2π/9) x_2=4.42 sin⁡(100πt-2π/5) You are required to determine the followings for the vibration of this beam: i. State the amplitude, phase angle, frequency and periodic time of each of these waves. ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? iii. At what time does each vibration first reach a displacement of −2??? iv. Use the compound angle formulae to expand x_1 and x_2 into the form ? sin 100?? ± ? cos 100??, where ? and ? are numbers to be found. v. Using your answers from part iv, express x_1+x_2 in a similar form. Convert this expression into the equivalent form ? sin (100?? + α)
4 helical springs is used in a suspension system of a motorcycle. The mean coil diameter is 15 cm, spring constant is 40,000 N/m, shear modulus = 80x10^9 N/(m^2), and has 8 effective turns. Determine what must be the wire diameter of the helical spring.

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