τ⃗ = r⃗ × F⃗_{g} + r⃗ × T⃗

τ⃗ = |L| |mg| sin(θ) into page

τ⃗ ≃ |L| |mg| θ into page

τ = −Lmg θ

I = mL^{2}

mL^{2} α = −Lmg θ

α = − (\frac{g}{L}) θ

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

ω = \sqrt{\frac{g}{L}}

\frac{d^{2}θ}{dt^{2}} = −ω^{2} θ

θ(t) = A cos(ωt + ϕ)

P = \frac{2π}{ω} = 2π \sqrt{\frac{L}{g}}

g = \frac{4π^{2}L}{P^{2}}

P^{2} = (\frac{4π^{2}}{g} ) L

τ⃗ = R⃗ × F⃗_{g} + 0 × T⃗

τ⃗ = |R| |mg| sin(θ) into page

τ⃗ ≃ |R| |mg| θ into page τ = −Rmg θ

I α = −Rmg θ

I = I_{Center of Mass} + mR^{2}

I = \frac{1}{2} mR^{2} + mR^{2} = \frac{3}{2} mR^{2}

\frac{3}{2} mR^{2} α = −Rmg θ

α = − (\frac{mgR}{I}) θ

\frac{d^{2}θ}{dt^{2}} = − (\frac{mgR}{I}) θ

ω = \sqrt{\frac{mgR}{I}}

\frac{d^{2}θ}{dt^{2}} = −ω^{2} θ

θ(t) = A cos(ωt + ϕ)

P = \frac{2π}{ω} = 2π \sqrt{\frac{L}{g}}

g = \frac{4π^{2}L}{P^{2}}

P^{2} = (\frac{4π^{2}}{g} ) L