E1 = (w1^2 - w^2)/((w1^2 - w^2)^2 + G^2 w^2)

E2 = (w2^2 - w^2)/((w2^2 - w^2)^2 + G^2 w^2)

A1 = G w/((w1^2 - w^2)^2 + G^2 w^2)

A2 = G w/((w2^2 - w^2)^2 + G^2 w^2)

G = 5

\(\(w1 = 3
\)\)

w2 = 6

elasa = E1 + E2

elasb = E1 - E2

absoa = A1 + A2

absob = A1 - A2

psia = elasa Cos[w t]  +  absoa Sin[ w t]

psib = elasb Cos[w t]  +  absob Sin[ w t]

Plot [{psia /. w -> 20, psib /. w -> 20}, {t, 0, 4}, 
      PlotStyle -> {Hue[0.9], Hue[0.7]}]