Derive the equation of motion and find the natural frequency of the system shown below (1)...
Tutorial Problem Draw the free-body diagram and derive the equation of motion in terms of 0 using Newton's second law of motion of the systems shown in Figure below. Derive the equation of motion using the principle of conservation of energy Pulley, mas moment of inertia at) Tutorial Problem Draw the free-body diagram and derive the equation of motion in terms of 0 using Newton's second law of motion of the systems shown in Figure below. Derive the equation of...
Use only newtons method and make free body diagram Derive the equation of motion and find the natural frequency of the system shown below. Given that the moment of inertial of the bar about its centre of gravity is Jg = 1 ml? 4 Uniform rigid bar, mass m 3K @ooo k 4 4 2 Hint: the moment of inertia of the bar about O is to be found first.
PROBLEM 3: (40 points) A rigid massless lever ACB, as shown in Figure 3, is pivoting about point C. A mass mis attached at point A. Assume frictionless pivot point, frictionless pulley, massless pulley, and small angles. The parameters are Ki-30N/m, m=1 kg, K2-40N/m, C-4.35N-s/m, L=0.4 m, a=0.2 m, and b=0.15 m. (i) Draw the Free Body Diagram (FBD) (5 points). (ii) Use Newton's approach to derive the equations of the motion (10 points). (iii) Use Lagrange's method to derive...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies 1 Q2. Figure 2 shows a system in which mass...
1. Derive the equations of motion of the system shown in Fig 1 by using Lagrange's equations. Find the natural frequencies and mode shapes of the dynamical system for k 1 N/m, k-2 N/m, k I N/m, and mi 2 kg, m l kg, m -2 kg. scale the eigenvectors matrix Ф in order to achieve a mass normalized eigenvectors matrix Φ such that: F40 Fan Fig. 1
Problem 7 - Vibration (10 pts) Determine the equation of motion and natural frequency wn of vertical oscillations of the cylinder of mass m. the mass and friction of the stepped drum are negligible. T 2r m
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod is also pinned to a roller and held in place by two elastic springs with constants k . Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid...
Using the energy method, try to derive the equation of motion for system shown in the Figure.
3.26 For the base-excitation prototype shown in Figure 3.6, assume that the base dis- placement y() is known, choose x(t) equation of motion by using Lagrange's equations. as the generalized coordinate, and derive the Package т тх Y k К(х — у) с(х — у) X о Base Figure 3.6. Base excitation and the free-body diagram of the mass -> 172