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3(a). Find the equations of motion for the system shown below. The system is two degree...
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)...
1. For the system shown in Figure 1. in determine the equations of motion taking degrees of freedom 01,02, X3, moment of inertia of slender rod about the center is 1G = m (10 points). 3 to m ki . > K2 Figure 1 Figure 1
The equations of motion for an undamped 2 DOF system are shown below. Find the transfer function X1/F2. You do not need to find the other three transfer functions. 5. 2 2+k3 )x2 = F2 dt-
The equations of motion for an undamped 2 DOF system are shown below. Find the transfer function X1/F2. You do not need to find the other three transfer functions. 5. 2 2+k3 )x2 = F2 dt-
The equations of motion for an undamped 2 DOF system are shown below. Find the transfer function X1/F2. You do not need to find the other three transfer functions. 5. 2 2+k3 )x2 = F2 dt-
The equations of motion for an undamped 2 DOF system are shown below. Find the transfer function X1/F2. You do not need to find the other three transfer functions. 5. 2 2+k3 )x2 = F2 dt-
1. Please derive the equation of motion of the system shown below. Assumptions: The bar is massless, the angle of rotation is small, and m is a point-mass. [30 marks] ki OW0000 k2 Figure 1
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...
(5 marks) Write the equation of motion for the double pendulum system shown below. Assume that the displacement angles of the pendulum are small enough to ensure that the spring is always horizontal. The pendulum rods are taken to be massless, of length I, and the springs are 75% of the way down the rods. 3. k, m2
4. Derive the equations of motion for the shown two degrees system in terms of x and ?. Bonus 12.5 Pts: Derive and solve the characteristic equation for l = 4 m, m = 3 kg, ki-1 N/m, and k2 = 2 N/m. .
please use mathematica for code NOT MATLAB
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system as shown below (in the figure on the left) with mi m2 and L1 L are The solutions are graphed below (on the right) for the initial conditions θι (0) 2, θ1(0) 1.02(0) 0, and 02(0)-0 for oS t s 50. (a) Reformulate the IVP as a first order system.2 (b) Generate approximate solutions using any method (Euler, improved...
The system shown below is made up of one mass and two inertia's (M, I1, and I2). Mass M is connected to Inertia I2 by a damper Ci that is pivoted at each end. The system outputs are y and 0, and the input is force F. At the equilibrium position shown all of the springs are unstretched. Therefore for this problem the initial spring forces are zero and may be neglected. Find the governing differential equations of motion in...