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1. Homework Statement
Two blocks of equal mass, m, are connected by a light string that passes over a massless pulley. One block hangs below the pulley, while the other sits on a frictionless horizontal table and is attached to a spring of constant k. Let x=0 be the equilibrium position of the block on the table.
a.) Determine the lagrangian of the system.
b.) Determine the equation of motion.
c.) Show that a particular solution of the equation of motion is x_{p} = A. where A is a constant, and determine A. Add this solution to the solution for the homogeneous equation and show that for the initial condition x = xdot = 0 at t = 0, the full solution is x = A(1  cos(wt)) and determine w. Recall that for an inhomogeneous differential equation that the solution is the sum of the homogeneous solution, x_{h}, and the particular solution.
2. Homework Equations
L = T  V
L = ∂L/∂x  d/dt(∂L/∂xdot) = 0
3. The Attempt at a Solution
I attempted part a and b, and im not really sure if what i got so far is correct. I also dont know how to start for part c. My work is in the attachment
Two blocks of equal mass, m, are connected by a light string that passes over a massless pulley. One block hangs below the pulley, while the other sits on a frictionless horizontal table and is attached to a spring of constant k. Let x=0 be the equilibrium position of the block on the table.
a.) Determine the lagrangian of the system.
b.) Determine the equation of motion.
c.) Show that a particular solution of the equation of motion is x_{p} = A. where A is a constant, and determine A. Add this solution to the solution for the homogeneous equation and show that for the initial condition x = xdot = 0 at t = 0, the full solution is x = A(1  cos(wt)) and determine w. Recall that for an inhomogeneous differential equation that the solution is the sum of the homogeneous solution, x_{h}, and the particular solution.
2. Homework Equations
L = T  V
L = ∂L/∂x  d/dt(∂L/∂xdot) = 0
3. The Attempt at a Solution
I attempted part a and b, and im not really sure if what i got so far is correct. I also dont know how to start for part c. My work is in the attachment
Attachments

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