pls answer question a and b sir pls use this matrix num sir (ad 200153)
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pls answer question a and b sir
pls use this matrix num sir (ad 200153)
subject (vibration)
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Solved in 2 steps with 2 images
- Figure Q3(b) shows a uniform bar AB of mass = 8 kg hinged at point C. Point A is connected to a spring to maintain the bar in vertical direction, and the stiffness k = 500 N/m. If point A is displaced counter-clockwise by a small angle θ = 3.5 degree and released, (i) With the free body diagram and kinetic diagram, determine the initial horizontal displacement of A.Figure Q2 shows two configurations of a part sorting machine in a production process. Since the process involve high speed movement, the design engineer have proposed two configurations of design as shown in Figure Q2 (a) – Configuration 1 and Figure Q2 (b) – Configuration 2. The mass m1 and m2 are 180 kg and 70 kg respectively and the spring coefficient, k = k1 = k2 = k3 = k4 = 300 N/m.(a) Sketch the Free Body Diagram for each configuration (Configuration 1 and Configuration 2).(b)Construct the Equation of Motion for each configuration (Configuration 1 and Configuration 2).(c)Predict which configuration that would lead to the highest first natural frequency, ωn1. State the reason for your answer.(d)Validate your answer in Q2(c) by providing natural frequency ωn calculation for each configuration.Consider the system formed by three ideal springs, a rigid rod of negligible mass and a body of mass M, as illustrated in the figure. The two springs attached to the ceiling are identical and have spring constant K1 = 2 kg/s2 and natural length L1 = 10 cm, while the third has spring constant K2 = 3 kg/s2 and natural length L2 = 20 cm. Assume that the mass M and the rod oscillate only along the vertical x-axis and that the gravitational acceleration is uniform with magnitude g=10 m/s2. What is the mass oscillation period? Choose the closest value.
- For the single DOF mass-spring system shown in Fig. Q5.a, determine the equivalent springconstant of the system. Assume k1=k2=35 N/m, k3=k4=55 N/m, k5=70 N/m, and k6=20 N/m.In the system in the figure, the static equilibrium position of the thin, slender homogeneous rod of mass m and length L is horizontal.During the movement of the system, the bar is separated from the horizontal by small angles. (A makes oscillating motion with small angles relative to the simple support point)a) Find the equation of motion of the system in terms of the given parameters.b) Since M=4 kg, m=1 kg, L=1 m, k=600 N/m, c=200 Ns/m, F=300 N, w=4 rad/s, is there resonance in the system? If there is resonance, what would you recommend to get rid of resonance?Consider the mass spring system shown in the figure below. The system is subject to a time dependent force
- In the system shown in Figure 1, assume that the rod pivoted at point P is massless and perfectly rigid. A mass m is attached to the other end of the rod and supported by a damper at distance L, and a spring at a distance L2 to the pivot point P. The displacement x of the mass is measured from the equilibrium position of the system. Assuming that x is small, obtain the equation of motion of the system by applying Newton's laws.A truck of mass 15000 kg traveling at 1.6m/sec impacts with a buffer spring, which compresses 1.25mm per kN. Find the maximum compression of the spring. ( No shortcut please)Under some circumstances, when two parallel springswith constants k1 and k2 support a single mass, theeffective spring constant of the system is given byk 4k1k2/(k1 + k2). A mass weighing 20 pounds stretchesone spring 6 inches and another spring 2 inches. Thesprings are first attached to a common rigid supportand then to a metal plate. As the figure illustrates(see image), the mass is attached to the center of the plate in the distributiondouble spring. Determine the constant of theeffective spring for this system. find the equationof motion if the mass is initially released fromequilibrium position with downward speed of2 ft/sec.
- In the mechanical system in the figure, a rigid rod is bedded at point P and has mass m at its end. can rotate vertically. At the other end of the rod, a spring (k) and a damper (c) are attached. Draw the Free-Body Diagram of the system, obtain the Equation of Motion (the vertical position of the ball We assume that the displacement x is very small and the bar is massless).From the following diagram find with k1=20N/m, k2=30 N/m, k3=25 N/m, k4=35 N/m, k5=50N/m and k6=60N/m, m=10kg A) the equivalent spring B) the displacement C) the work performedA general basic vibratory system consists of mass and spring. Figure Q1 shows thevibration knowledge application of multiple parallel springs installed in between theCaterpillar diesel engine generator and the foundation slab (inside the red dash box).Given that the mass of the diesel engine generator is W = 400 kg, the spring equivalentstiffness is k eq = 1x10^6 N/m and the generator revolution per minute is RPM = 3200 RPM.Assume that the system is a single degree of freedom and undergoes only verticaltranslational movement. -Sketch free body diagram of the system together with the action and reactionforce magnitude and direction. -Compare the value of spring displacement, x for the free vibration and forcevibration of 10 kN if the diesel engine generator excites 1 m/s2during operation. Neglect the gravitational effect. -Determine the number of cycles per second for the diesel engine generator.