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Homework Statement
A system consists of 3 identical masses (A,B & C) in a line, connected by 2 springs of spring constant k. Motion is restricted to 1 dimension. at t=0 the masses are at rest. Mass A is the subjected to a driving force given by:
F=F0*cos(omega*t)
Calculate the motion of C
Homework Equations
L=T-V, Euler lagrange equation.
The Attempt at a Solution
I figured that the easiest way to do this is to write a lagrangian and solve for the equation of motion for the masses.
I denoted the initial positions of the masses x1, x2 and x3 respectively.
the kinetic energy term for the lagrangian then becomes
T= 1.5*m*((x1dot)^2 + (x2dot)^2 + (x3dot)^2)
For the potential, i have stated that the distance between the masses at equilibrium is equal to J. Hence the potential due to the springs is:
V= k(x1^2 + 2*x2^2 - 3*x2*x1 - x2*x3 + x1*x3 + J(x1+x3-2*x2)
I am unsure if this is correct and i have no idea how to incorporate the driving force into the equation. Any ideas?