Please Use Energy Methodd/dt (T+V) where T is KE and V is PE 3.21. A uniform slender rod of mass m and length I is hinged at point 0, as shownin Fig. P3.10. The rod is attached to a spring and a damper at one end and todamper at the other end, as shown in the figure. If k = 4000 N/m, m = 10kg,3 Free Vibration126ci = c2 = 20N - s/m, and I = 5 m, find the complete solution provided thatthe rod has zero initial angular displacement and an initial angular velocity of5 rad/s.1/321/3C2Fig. P3.10

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Answered: 3.21. A uniform slender rod of mass m…

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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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.
Problem 2. A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, as shown in Figure 2. End P of spring PQ is subjected to a sinusoidal displacement, x(t) = x,sinwt. 1=1 m, k=1000 N/m, m=10 kg, xo=1 cm, and w=10 rad/s. a) Drive the equations of motion and find the natural frequency of the bar b) Find the steady-state angular displacement of the bar Vont do Simulate the system and plot displacements for the following cases (choose suitable simulation time for each case): 1) With the initial conditions theta0=thetad0=0, an excitation x=xesin(wt) is applied vertically at point P. Choose such w values so that the system is in resonancer experiencing beating. i. D ii. xt t) = xo sin wt Uniform bar, k mass m Figure 2. Spring-mass system
Problem 2. A uniform bar of mass m is pivoted at point O and supported at the ends by two springs, as shown in Figure 2. End P of spring PQ is subjected to a sinusoidal displacement, x(t) = x,sinwt. 1=1 m, k=1000 N/m, m=10 kg, xo=1 cm, and w=10 rad/s. a) Drive the equations of motion and find the natural frequency of the bar b) Find the steady-state angular displacement of the bar Simulate the system and plot displacements for the following cases (choose suitable simulation Vont time for each case): 1) With the initial conditions theta0=thetad0=0, an excitation xEsin(wi) Is applied vertically at point P. Choose such w values so that the system is i. in resonance, exPeriencing beating. do D ii. (1) = xo sin wt Uniform bar, mass m 31 Figure 2. Spring-mass system
Q4/ For the figure below the spring is used to stop a 10 kg package. If the maximum deflection in the spring is 70 mm, (a) the total work of the system in the figure below is: 8m/s H=0,25 /K=400N/m 10kg 500m 0-30 (b): The total work when theta =0 equal to: *
3) Consider this car, which can be modelled as a rigid bar with its centre of mass C.G. not coinciding with its geometric centre (m= 1000kg, 11m; /2 = 1.5m ), and supported by two springs, k = kx=20kN/m, as shown in Figure Q1 (a) Describe the system in term of degree of freedoms (b) Draw the free body diagram for the system to derive the equations of the vibration motion (c) Determine the mass matrix and stiffness matrix of the system. (d) Determine the nature frequencies of the system Bounce C.G. Pitch -1/2- Figure Q1
Please show all work!
3. Consider the spring-mass system in an elevator that moves vertically. The natural length of the spring is as shown in the figure below, and at time t=0 the elevator starts moving with prescribed displacement y(t). Suppose that the relative displacement of the mass is x(t), i.e., its displacement with respect to the elevator. Assume mass m can only move vertically, the elevator is massless, and gravity is included. a. Derive the equation of motion of the mass using Newton's 2nd law. b. When is the mass in the elevator in a condition of effective "zero gravity"? y(t) x(t)
pls ans quickly take p= 2 q=0 r=1
Question in pic.
P
5. A rod of length L, Young's modulus E, cross-sectional area A and mass density p is installed as shown. Suppose m = pAL and kL / EA =1. Find the equations of motion Open Question m www f(t) x=0 x = L/2 x= L
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.

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