- #1

Elvis 123456789

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## 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 = x-dot = 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.

## Homework Equations

L = T - V

L = ∂L/∂x - d/dt(∂L/∂x-dot) = 0

## The Attempt at a Solution

I attempted part a and b, and I am not really sure if what i got so far is correct. I also don't know how to start for part c. My work is in the attachment