mecànica de una caisha estirada per una força vertical

F = at^{n}


m·d_{tt}^{2}[y(t)] = F+(-1)·qg


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


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


y(t) = (1/m)( ( a/((n+1)(n+2)) )t^{n+2}+(-1)·(1/2)·qg·t^{2} )
y(t) = (1/m)( ( a/((n+1)(n+2)) )t^{n}+(-1)·(1/2)·qg )·t^{2}


y(t) = 0 <==> ( t_{0} = 0 or t_{k} = ( (1/2)·qg·( ((n+1)(n+2))/a ) )^{(1/n)} )


d_{tt}^{2}[y(t_{k})] = (1/m)·qg·( (1/2)(n+1)(n+2)+(-1) )


d_{t}[y(t_{k})] = (1/m)·qg·( (1/2)(n+2)+(-1) )·( (1/2)·qg·( ((n+1)(n+2))/a ) )^{(1/n)}