oscilador harmónic forçat resonància

m·d_{tt}^{2}[x(t)]+k·x(t) = F·sin(vt)

d_{tt}^{2}[x(t)]+u^{2}·x(t) = (F/m)·sin(vt)

x(t) = (F/m)·( 1/(u^{2}+(-1)·v^{2}) )·sin(vt)

m·d_{tt}^{2}[x(t)]+k·x(t) = F·sin((-v)t)

d_{tt}^{2}[x(t)]+u^{2}·x(t) = (F/m)·sin((-v)t)

x(t) = (F/m)·( 1/(u^{2}+(-1)·v^{2}) )·sin((-v)t)

m·d_{tt}^{2}[x(t)]+b·d_{t}[x(t)]+k·x(t) = F·( sin(vt)+sin((-v)t) )

d_{tt}^{2}[x(t)]+(b/m)·d_{t}[x(t)]+u^{2}·x(t) = (F/m)·( sin(vt)+sin((-v)t) )

x(t) = (F/m)·( 1/(u^{2}+(-1)·v^{2}) )·( sin(vt)+sin((-v)t) )