mecànica clàssica

F = ke^{at}


m·d_{tt}^{2}[x(t)] = ke^{at}
d_{tt}^{2}[x(t)] = (k/m)·e^{at}


d_{t}[x(t)] = ( k/(am) )·e^{at}


x(t) = ( k/(a^{2}m) )·e^{at}


E(t) = ∫ [ ke^{at} ] d[x]
E(t) = ∫ [ ke^{at}·d_{t}[x] ] d[t]
E(t) = ∫ [ ke^{at}·( k/(am) )·e^{at} ] d[t]
E(t) = ∫ [ ( k^{2}/(am) )·e^{2at} ] d[t]


E(t) = ( k^{2}/(2a^{2}m) )·e^{2at}


(m/2)·d_{t}[x(t)]^{2} = ( k^{2}/(2a^{2}m) )·e^{2at}