Physics - Advanced Classical Mechanics - Lagrangian mechanics - Lagrangian Problems

5 problems. P1: 'Mass on a spring: x from equilibrium. T = ½mẋ², V = ½kx². L = ½mẋ² - ½kx². E-L: d/dt(mẋ) - (-kx) = 0 → mẍ + kx = ___' (0 - SHM!). P2: 'Simple pendulum: T = ½ml²θ̇², V = -mglcosθ. ∂L/∂θ̇ = ___' (ml²θ̇). P3: 'd/dt(ml²θ̇) = ml²θ̈. ∂L/∂θ = ___' (-mglsinθ). P4: 'E-L equation: ml²θ̈ + mgl