d 2 x d t 2 + k m = 0 {\displaystyle {\frac {d^{2}x}{dt^{2}}}+{\frac {k}{m}}=0} s 2 + k m = 0 {\displaystyle s^{2}+{\frac {k}{m}}=0} s = ± − k m t {\displaystyle s=\pm {\sqrt {-{\frac {k}{m}}}}t} s = ± j ω t {\displaystyle s=\pm j\omega t} x = e ( ± j ω t ) {\displaystyle x=e^{(\pm j\omega t)}} x = e ( j ω t ) + e ( − j ω t ) {\displaystyle x=e^{(j\omega t)}+e^{(-j\omega t)}} x = A S i n ω t {\displaystyle x=ASin\omega t}
d 2 y d t 2 + k m = 0 {\displaystyle {\frac {d^{2}y}{dt^{2}}}+{\frac {k}{m}}=0} s 2 + k m = 0 {\displaystyle s^{2}+{\frac {k}{m}}=0} s = ± − k m t {\displaystyle s=\pm {\sqrt {-{\frac {k}{m}}}}t} s = ± j ω t {\displaystyle s=\pm j\omega t} y = e ( ± j ω t ) {\displaystyle y=e^{(\pm j\omega t)}} y = e ( j ω t ) + e ( − j ω t ) {\displaystyle y=e^{(j\omega t)}+e^{(-j\omega t)}} y = A S i n ω t {\displaystyle y=ASin\omega t}
θ ( t ) = θ 0 cos ( g ℓ t ) | θ 0 | ≪ 1 {\displaystyle \theta (t)=\theta _{0}\cos \left({\sqrt {g \over \ell }}t\right)\quad \quad \quad \quad |\theta _{0}|\ll 1}
