τ⃗ = r⃗ × F⃗_{g}

τ⃗ = L⃗ × (mg⃗)

τ⃗ = mgL sin(θ)

τ⃗ = mgL sin(θ) (into page)

I = mL^{2}

τ⃗ = Iα⃗

α⃗ = \frac{τ⃗}{I}

α⃗ = (\frac{g}{L}) sin(θ) (into page)

α⃗ = (\frac{g}{L}) θ (into page)

α⃗ = − (\frac{g}{L}) θ⃗

\frac{d^{2}θ⃗}{dt^{2}} = − (\frac{g}{L}) θ⃗

\frac{d^{2}x⃗}{dt^{2}} = − (\frac{k}{m}) x⃗

θ(t) = A cos(ωt + ϕ)

ω = \sqrt{\frac{g}{L}}