1. The problem statement, all variables and given/known data The problem states that a pendulum is attached to a spring that can only oscillate in the vertical direction. I am supposed to derive equations of motion for the spring/pendulum system under my chosen generalized coordinates. 2. Relevant equations Lagrange equations of motion 3. The attempt at a solution I choose a to describe the system by the height of the pendulum mass and the angle at which it swings. So the two coordinates are y and θ, respectively. Given a spring constant, k, and the assumption of a massless spring, I formulated the potential energy of the system to be: U = (1/2)ky^2+mg(y-l*cos(θ)) where l is the length of the pendulum, and I have chosen the potential to be zero at y = 0 & θ = pi/2. The kinetic energy of the system should be that given only by the mass of the pendulum. I formulated this to be: T = (1/2)m((vx)^2 + (vy)^2) = (1/2)m((l*θ'*cos(θ))^2 + (y' + l*θ'*sin(θ))^2) Without attempting to put up all the math on the board, I computed the Lagrange equations on y and θ, and found the two differential equations: y'' + (k/m)y +l*θ''*sin(θ) + l*(θ')^2*cos(θ)+g = 0 and θ'' + (1/l)y''*sin(θ) + (1/l)*g*sin(θ) = 0 I am unsure if I have made any mistakes, but am I going about this problem at all correctly? Thanks.