Determine equations of motion for the system using the generalized coordinates theta1, theta2 as shown. Each bar has a mass of m. A horizontal force F is applied to the end of the 2 bar system. 5) Determine the equations of motion for the system using the generalized coordinates ???2 as shown. Each bar has a mass of m. A horizontal force Fis applied to the end of the 2 bar system. o,
Equations of Motion: Lagrange's Method Use Lagrange's Method to find the Equations of Motion for the following systems. Define a datum point at the static equilibrium point, solve for the initial spring forces, and substitute them in to get simplified answers. M M
5. (10 points) Obtain the state model for the two-mass system whose equations of motion are given below. The function f(t) is the input to the system. Identify the A and B matrices.
Problem # 2 (50pts) m2 Find the equations of motion to describe the system below. The spring produces zero force at zero length. The spring has zero mass, the rod has zero mass. Note: To describe the dynamics, you need 2 Generalized coordinates: 0,x. u g a) Find the velocities of the important components, mi, m2, (10 points). mi b) Find the kinetic energy of the system (10 points). c) Find the potential energy of the system (10 points). d)...
Problem 4*: (Motion along a spiral) A particle of mass m moves in a gravitational field along the spiral z = k0, r = constant, where k is a constant, and z is the vertical direction. Find the Hamiltonian H(z, p) for the particle motion. Find and solve Hamilton's equations of motion. Show in the limit r = 0, 2 = -g.
Problem 5: For the system shown below, write the differential equations for small motions of the system, in terms of the degrees of freedom (x(t),() Mass of the bar is m, and mass of the block is also m. System is set into motion through suitable initial conditions. Once you find the equations of motion in terms of the respective degrees of freedom, write out the natural frequency and the damping ratio for each sub-system, respectively. Problem 5: For the...
Find the equations of motion using D’alembert principle.
[+10 points) Find the parametric equations for the graphs below: a. [+5 points] Uniform circular motion, counterclockwise. Include interval for t to sketch out given portion below. y 2 X 2 b. [+5 points] Linear motion from (1,0) to (0,3 ). Include an interval for t to sketch out given portion below: y 2+ X
Find the Hamiltonian and Hamilton’s canonical equations of motion for the systems described in both parts of the above problem. Two blocks of equal mass m are connected by a flexible cord. One block is placed on a smooth horizontal table, the other block hangs over tire edge. Find the acceleration of the blocks and cord assuming (a) die mass of die cord is negligible and (b) the cord is heavy, of mass m'.
2. The equations of motion for a system of reduced mass moving subject to a force derivable from a spherically symmetric potential U(r) are AF –102) = (2+0 + rē) = 0 . (3) Using the second of these equations, show that the angular momentum L r 8 is a constant of the motion (b) Then use the first of these equations to derive the equation for radial motion in the form dU L i=- What is the significance of...