Using Lagrange’s Method, select a set of coordinates, identify any constraint equations, and determine the equations of motion for the adjacent figure. Assume there is no slippage between the cord and the pulley.
Using Lagrange’s Method, select a set of coordinates, identify any constraint equations, and determine the equations...
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,
Please use Lagrange's Equation and solve both parts. 2. (30 Points) For the figure shown below, find the equations of motion by Lagrange's equations. Assume that all variables are measured from static equilibrium. (20 Points) Determine the condition under which the steady-state displacement of the mass m will be zero. Assume the Disc of mass M is described by the coordinate and has mass moment of inertia J. Disc, mass M Rolls without slipping Pulley Cord Fisin (0) Figure 2:...
To set up and solve the equations of motion using rectangular coordinates The 2-kg collar shown has a coefficient of kinetic friction uk= 0.18 with the shaft. The spring is unstretched when s=0 and the collar is given an initial velocity of vo = 17.1 m/s. The unstretched length of the spring is d=1.2 m and the spring constant is k=8.70 N/m. Part B - The acceleration of the collar after it has moved a certain distance What is the...
Equations of Motion: Rectangular Coordinates a,--150 m Learning Goal To set up and solve the equations of motion using rectangular coordinates The 2kg collar shown has a coeficient of kinesic friction Correct = 0.2 wit, the shut The spring is urstre ed aren s :0 and the collar is given an initial velocity of to 19.6 m/s The unstretohed length of the spring is d-1.1 m and the spring constant is 423 N/m part C . The speed of the...
Using Lagrange's method, find the equations of motion for: a) A simple Atwood machine. b) A particle that slides along a smooth inclined plane.
double integration method Q2 Determine the equations of the elastic curve using the coordinates x, and x2, specify the slope and deflection at B. EI is constant. W To A B -X147 a - X2 |--X3 L
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...
Part B and C <Problem Assignment No. 2 Equations of Motion: Rectangular Coordinates Learning Goal: To set up and solve the equations of motion using rectangular coordinates. The 3.5-kg collar shown has a coefficient of kinetic friction μk 0.195 with the shaft. The spring is unstretched when s 0 and the collar is given an initial velocity of vo 10.3 m/s. The unstretched length of the spring is d- 1.3 nm and the spring constant is k- 3.13 N/m. (Figure...
QUESTION 2, Determine the equations of the elastic curve using the coordinates the x1 and X2, specify the slope and deflection at B. El is constant w A B a X2 L o
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...