L-Shaped Pendulum Differential Equation
Two thin rods, each of length L and mass m, are welded together to form an L-shape. The resulting object is pivoted at the free end of one rod and oscillates as a compound pendulum. For small-angle oscillations, which of the following second-order differential equations correctly describes the motion?
A
d²θ/dt² + (3g√2)/(4L) θ = 0
B
d²θ/dt² + (2mg/m)(L/2)/(2L²/3)·θ = 0
C
d²θ/dt² + (2mg/m)(L/2)/(L²)·θ = 0
D
d²θ/dt² + (mg/m)(L)/(L²)·θ = 0
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