2.22 A scissors jack is used to lift a load W. The links of the jack are rigid and the collars can slidefreely on the shaft against the springs of stiffnesses k₁ and k₂ (see Fig. 2.63). Find the naturalfrequency of vibration of the weight in the vertical direction.Jeccceek₁CollarTOWShaftLink1FIGURE 2.63 Weight lifted by scissors jack.Collark₂

To Find : The natural frequency of vibration of the weight in the vertical direction Given : The…

Answered: 2.22 A scissors jack is used to lift a…

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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3.58 A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, as shown in Fig. 3.59. End P of spring PQ is subjected to a sinusoidal displacement, = xo sin cot. Find the steady-state angular displacement of the bar when / = 1 m, k = 1000 N/m, m = 10 kg, xo = 1 cm, and = 10 rad/s.
Vibration
ANSWER ALL QUESTIONS OTHERWISE DONT ATTEMPT IT STRICTLY.
Statics an 2.18 A 200# stone is being lifted off the ground by a lev- ering bar. Determine the push P required to keep the stone in the position shown. Varignon's Theorem The French mathematician Pierre Varignon developed a very important theorem of statics. It states that the mo- ment of a force about a point (axis) is equal to the algebraic 1W=200* 3011 36" 47
Two massless springs with different spring constants k₁= 100 N/m and k₂ = 10 N/m are aligned vertically, as shown in figure 1. A block of mass m = 0.12 kg is placed on the bottom spring. The distance between the top of the box and the top spring is h = 0.35 m. You compress the bottom spring Ay = 0.3 m from its equilibrium position (figure 2). When you let go, the box flies up (figure 3) and compresses the top spring (figure 4). Treat the upward direction (↑) as positive, such that the compression of the top spring is a positive displacement. What is the maximum compression of the top spring due to the flying box? Give your answer in units of meters to 2 decimal places. Use g = 9.8 m/s^2. Assume air resistance is negligible. T h EW Ay (2) www Backup link to image (opens in new tab). fumand M риту 4 ² ↑ M ? www
7. The arrangement in the drawing shows a block (mass = 14.0 kg) that is held in position on a frictionless incline by a cord (length = 0.582 m). The mass per unit length of the cord is 1.30 x 10-2 kg/m, so the mass of the cord is negligible compared to the mass of the block. The cord is being vibrated at a frequency of 166 Hz (vibration source not shown in the drawing). What is the smallest angle 0 between 15.0° and 90.0° at which a standing wave exists on the cord?
III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.
Calculate the equivalent spring equation and linear spring. Theory of vibration
igure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y 0, and the springs are in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. DE only 225 Your tasks: X k 0 3k a F a M y A Derive an equation of motion for the system in terms of the angular displacement 0, and its derivatives (you should not have y or its derivatives in this equation.) B Derive an equation of motion for the system in terms of the displacement y, and its derivatives (you should not have or its derivatives in this equation. C Assuming there is no external actuator force F acting on the system, write down the total energy H of the system in terms of 0,0 and element constants. Derive an expression for the time derivative H of the total energy. D Transform the equation from part B, which is in y, to another…
1- Two mass-spring-damper systems A & B. System A has = 0.1 and @n = 20 rad/sec, and system B has < = 0.3 and wn = 5 rad/sec. Which system will vibrate longer in time? Why?
7. A spring is attached to the floor. When a 125 g mass is placed on top of the spring it compresses by 0.26 m. What is the spring constant of this spring?
As illustrated in the figure below, the bedplate of an experimental diesel engine is supported on four springs to isolate the vibrations from the test frame. The effective weight of the diesel engine and bedplate is 43kg and the stiffness of each of the four springs is 250 kN/m. Using a simplified approach - by applying Newton's Second Law assuming a single degree of freedom system and ignoring damping - what rotational engine speed is best avoided? Bedplate Test engine Supporting springs Figure: Sketch of a test engine mounting arrangement Give your answer in rad/s to 1 decimal place.

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