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Using Lagrangian to derive the equation of motion

  1. Feb 12, 2017 #1
    1. The problem statement, all variables and given/known data
    derive the equation of motion of a mass-spring-pulley system using lagrange's equations. A mass m is connected to a spring of stiffness k, through a string wrapped around a rigid pulley of radius R and mass moment of inertia, I.

    2. Relevant equations
    kinetic energey
    T = 1/2 (m)(x_dot) + 1/2 (I)(theta_dot)
    potential energy
    V = 1/2 k(R)(x)


    3. The attempt at a solution
    20170212_201908.jpg
    sorry for the sideways picture... dont know why its doing that. but please help homework is due tomorrow morning! thanks!
     
  2. jcsd
  3. Feb 12, 2017 #2

    kuruman

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    What is your Lagrangian? Without writing it down, you will not be able to derive the equations of motion.
    It seems your generalized coordinates are x and θ. Is there a constraint relating the two?
     
  4. Feb 12, 2017 #3
    ts the second to last equation on the picture, with the partial derivatives to the respect of x. so ∂T/∂x⋅ - ∂T/∂x + ∂V/∂x = Q

    and i believe theres a onstraint of x = rθ
     
  5. Feb 12, 2017 #4

    kuruman

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    That's not the Lagrangian. The Lagrangian is L = T - V. What you have is the equation for generalized coordinate x. You need to write another such equation involving θ and apply the constraint relating x and θ to get a single equation of motion.
     
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