mecànica en un medi resistent

F_{x} = at^{n}


m·d_{tt}^{2}[x(t)] = F_{x}+(-1)·k·d_{t}[x(t)]


d_{tt}^{2}[x(t)] = (1/m)( at^{n}+(-1)·k·d_{t}[x(t)] )


d_{t}[x(t)] = (1/m)( ( a/(n+1) )t^{n+1}+(-1)·k·x(t) )


d_{t}[x(t)]+(k/m)·x(t) = (1/m)( ( a/(n+1) )t^{n+1} )


x(t) = e^{(-1)(k/m)t}·∫ [ (1/m)( a/(n+1) )t^{n+1}·e^{(k/m)t} ] d[t]