mecànica clàssica arrel cuadrada de la posició

m·d_{t}[x(t)] = a·( x(t) )^{(1/2)}


m·d_{tt}^{2}[x(t)] = (1/2)·a·( x(t) )^{(-1)(1/2)}·d_{t}[x(t)]


m·d_{tt}^{2}[x(t)] = (1/2)·(a^{2}/m)


d_{tt}^{2}[x(t)] = (1/2)·(a^{2}/m^{2})


d_{t}[x(t)] = (1/2)·(a^{2}/m^{2})·t


x(t) = (1/4)·(a^{2}/m^{2})·t^{2}


E(t) = ∫ [ ( (1/2)·(a^{2}/m) )·( (1/2)·(a^{2}/m^{2})·t ) ] d[t]


E(t) = (1/8)·(a^{4}/m^{3})·t^{2}


(m/2)·d_{t}[x(t)]^{2} = (1/8)·(a^{4}/m^{3})·t^{2}