F⃗ = −k x⃗

F⃗ = ma⃗ = m\frac{d^{2}x⃗}{dt^{2}}

m\frac{d^{2}x⃗}{dt^{2}} = −kx⃗

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

\frac{d^{2}x⃗}{dt^{2}} = −ω^{2} x⃗

x(t) = A cos (\sqrt{\frac{k}{m}}t + ϕ)

ω = \sqrt{\frac{k}{m}}

x(t) = A cos (ωt + ϕ)