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...
the cylinder mass m2 dan the inertia moment to horizontal axis O is Io. that stepped cylinder is rolling without slip on the horizontal surface. mass m1 is translatiom moving without friction. so find : a) the equation of motion from that system (EoM) b) the persoanl frequency (omega n) c) the attentuation's coefficient "c" ,that makes the system critically vague VCI TTTTTTTTTTT male
please solve it as soon as possible and be sure of your answers A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k. If the translational and angular displacements of the cylinder are x and 8 from its equilibrium position. Determine the following: a- Equation o method b- Find the natural frequency of vibration f motion of the system assuming that the system is...
Consider the system shown in the figure below. The mass moment of inertia of the bar about the point O is JO, and the torsional stiffness of the spring attached to the pivot point is kt . Assume that there is gravity loading. The centre of gravity of the bar is midways, as shown in the figure. Question 2 Consider the system shown in the figure below. The mass moment of inertia of the bar about the point O is...
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotational radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of 0, and 0 (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode Fosin shapes if m...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks with radius r and 2r, respectively, (1) Find its total kinetic energy, total potential energy and e, 2r Lagrangian in terms of θ' and θ, (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and Im In 4) Calculate the natural frequencies and the associated mode...
The Figure below shows a homogeneous cylinder of radius R and mass m. Assuming that the cylinder rolls on a rough surface without sliding, derive the equations of motion using the energy conservation approach, and determine the natural frequency. 179
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
question (c), (d), (e), (f) please. Thanks. 1 Consider a cylinder of mass M and radius a rolling down a half-cylinder of radius R as shown in the diagram (a) Construct two equations for the constraints: i rolling without slipping (using the two angles and θ), and ii) staying in contact (using a, R and the distance between the axes of the cylinders r). (b) Construct the Lagrangian of the system in terms of θ1, θ2 and r and two...
6. Consider the system shown: m, J, R The wheel with mass m, radius R, and rotational moment of inertia J rolls without slipping down the incline shown. The spring affixed to its axle has rest length h, and is neither extended nor compressed when r 0. The external force F is directed parallel to the direction of rolling. Find the total kinetic energy and potential energy in the system. Assume the gravitational potential energy to be zero when the...
Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of, and (2) Derive the equations of motion using Lagrangian equation method, (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode shapes if m-30 g, 4-8 x...