Three springs with different spring constants are connected as shown below. You are going to use spring elements to simulate this system. Suppose that the spring constants of the first, second and third elements are k1=3,410 N/m, k2=3,160 N/m and k3=3,380 N/m, respectively. Two horizontal forces are applied to the system (as shown) at nodes 2 and 3. Find the displacement of node 3 and write your answer in mm (millimetre).

Three springs with different spring constants are connected as shown below. You are going to use spring elements to simulate this system. Suppose that the spring constants of the first, second and third elements are k1=3,410 N/m, k2=3,160 N/m and k3=3,380 N/m, respectively. Two horizontal forces are applied to the system (as shown) at nodes 2 and 3. Find the displacement of node 3 and write your answer in mm (millimetre).

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

See similar textbooks

Similar questions

A weight W= 120 kN is being supported by steel sections with force T, force F, andforce C. The coordinates of A, B, C, and D are given. Assume that E is the origin(0,0,0). Determine Forces T, F, and C. (Hint: Produce three equations fromequilibrium of force system)Note: The Forces T, F, and C must be computed accurately to design the proper sizes ofsteel sections in the subject “Steel Design.”
k, k3 A В k2 What is the equivalent spring stiffness between the points A and B. If ki = 1 N/m, k2 =1 N/m. k3 = 2 N/m and k4 = 2 N/m A N/m
For this problem, take a look at Figure 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 spring is 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. k Schen a 0 a F The equation of motion for the system can be derived to be: a 4aM0+ ak0 =-F-2Mg T y M Your tasks: A. Transform the rotational equation of motion, which is in 0, given above, to another variable, y, which is zero at the static equilibrium position. B. Represent the mechanical system in state space form. Using MATLAB or a calculator (just say what you used), calculate the eigenvalues of your A matrix for the following system parameters: a = 0.25 [m], M = 1 [kg], k = 16 [N/m], and F = 0 [N]. What do the eigenvalues say about the stability of the system? C. Derive the response of the system in the…
For this problem, take a look at Figure 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 spring is 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. k Schen a 0 a F The equation of motion for the system can be derived to be: a 4aM0+ ak0 =-F-2Mg T y M Your tasks: A. Transform the rotational equation of motion, which is in 0, given above, to another variable, y, which is zero at the static equilibrium position. onical system in sta bace form. Using MATLAB or a calculator lues of INI. W 16 [N/m], and C. Derive the response of the system in the Laplace (s) domain. Use the static equilibrium value found in part A (Ost) as the initial value, (0), for the problem. Assume (0) and the force, F, are both zero. You may treat gravity as g = 10 [m/s²] for ease of…
1. In lecture I focused on a horizontal mass-spring system so we could ignore gravity, but in practice it's much easier to build a vertical mass-spring system. In the figure below, we can see a suspended spring with spring constant k both before and after a mass m is hooked to it. Y Yo yo is the equilibrium height of the spring (without the mass) and in the figure y = 0 is set at the ground. a) Using the coordinate system in the figure, show that Newton's second law for the hanging mass-spring system leads to the following differential equation: d²y dt² k (y - Yo) - g m b) Now define a new coordinate, y', related to y by a constant shift: y = y' + C, where C = constant. Show that if you choose the right value of C, Newton's second law is identical in form to a mass-spring system without gravity. What is the period of the system? c) Effectively, gravity just shifts the equilibrium position of the system, but the system still undergoes simple harmonic motion. What is the net force on the…
or 5, 2. You have a massless spring of force constant 64 N/m, but it is wound tightly enough that you must apply 16 N of force to it before it begins to stretch. You attach a 12 kg mass to one end of the spring. The other end is fixed in place above the mass (e.g. it is clamped to the room's ceiling). A second mass of 1.0 kg is connected to the bottom of this first mass via a thin string of negligible mass. The system is initially in equilibrium, but then the string connecting the smaller mass suddenly snaps. 2.1 What is the initial acceleration of the spring-mass system? 2.2. What is the amplitude of oscillation for this system? 2.3 What would be the period of oscillation for this system? 2.4 Determine the maximum value of the kinetic energy of the mass still connected to the spring. Assume negligible damping.
The image below is of an arm in 90 degree elbow flexion holding an implement in the hand. SOLVE FOR THE TORQUE ABOUT THE ELBOW IN ORDER TO MAINTAIN EQUILIBRIUM. Here are the values. d1: 0.024m d2: 0.310m d3: 0.690m Fbarbell: 697N Farm: 74N
Q1: In the below drawings, three unbalanced masses and related details are provided. Please answer the following questions. a) a balancing mass is to be located at rp = 50 mm, then what would be the balancing m1 m1 650 mm 200 mm m2 mass (m,) and its angular position (Op) (Please use the r2 m2 A graphical method) r3 m3 15 m3 b) If the system is not balanced what would be the reaction forces at A and B. (FA, FB=?) n = 150 rpm r; = 30 mm m, = 1 kg r2 = 20 mm 40 тm 13= m, =3 kg m; = 2 kg k = please choose an appropriate scaling factor yourself SHOT ON MI 6 MI DUAL CAMERA
Problem No 6 1.26 Find the equivalent spring constant of the system shown in Fig. 1.82. k F k k k FIGURE 1.82 Springs connected in series-parallel
GIVEN: DISTANCES CO= 7m BO= 7m OD= 8m AD= 8m GIVEN: WEIGHT W1= 195 N W2= 295 N GIVEN: ANGLE X= 55 Degree Y= 48 Degree SOLVE: (a) Tension at CB in NEWTON (b) Reaction at point O in NEWTON PLS PLS SOLVE AND SHOW COMPLETE SOLUTION AND WRITE LEGIBLY. ALSO, DRAW THE FREE-BODY DIAGRAM. ROUND OFF IN 4 DECIMAL PLACES.
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…
Q1: The system shown has two masses. Beam of mass (Jo#m L² kg.m²) rotates about fixed point (O) and its free end is connected to disk rotates about fixed point (O₂). Consider all connecting links are massless and rigid. Find 1- The displacements of points A, B, and C in addition to the rotations of masses, all in terms of 0. 2- Find the equation of motion (EOM) in terms of 0. 3- What is the natural frequency of the system? 0 L/2 8 Energy methods A Jo=m L²2 L/2 Joz-m R² R C B C 128