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Theoretical Physics

Derive the equation of motion for a Simple Harmonic Oscillator using the Lagrangian.

L = T - V = \frac{1}{2}m\dot{x}^2 - \frac{1}{2}kx^2

HINT:Apply the Euler-Lagrange equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}}) - \frac{\partial L}{\partial x} = 0$ to find the differential equation of motion.

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Derive the equation of motion for a Simple Harmonic Oscillator using the Lagrangian.

L = T - V = \frac{1}{2}m\dot{x}^2 - \frac{1}{2}kx^2

HINT:Apply the Euler-Lagrange equation

\frac{d}{dt}(\frac{\partial L}{\partial \dot{x}}) - \frac{\partial L}{\partial x} = 0

to find the differential equation of motion.