a_{y} = \frac{d^{2}y}{dt^{2}} =

y(t) = A cos (ωt + ϕ)

\frac{d f(x)}{dx} = A

\frac{d f(x)}{dx} = 0

\frac{d f(x)}{dx} = f(x)

\frac{d f(x)}{dx} = −f(x)

\frac{d f(x)}{dx} = Af(x)

\frac{d^{2} f(x)}{dx^{2}} = 0

\frac{d^{2} f(x)}{dx^{2}} = A

\frac{d^{2} f(x)}{dx^{2}} = Af(x)

\frac{d^{2} f(x)}{dx^{2}} = −Af(x)

\begin{aligned}I & = I_{com} + Mx^{2} \\ & = \frac{1}{12}ML^{2} + Mx^{2} \end{aligned}

τ = Mgx sin(θ)

\begin{aligned}α & = \frac{τ}{I_{tot}} \\ & = ( \frac{Mgx}{\frac{1}{12}ML^{2} + Mx^{2}} ) sin(θ) \end{aligned}

α⃗ ≃ − ( \frac{Mgx}{\frac{1}{12}ML^{2} + Mx^{2}} ) θ⃗

sin(θ) ≃ θ in radians

α = \frac{d^{2}θ}{dt^{2}}

\frac{d^{2}θ}{dt^{2}} ≃ − ( \frac{Mgx}{\frac{1}{12}ML^{2} + Mx^{2}} ) θ