Manipulate[
C1[Q0_, q0_, w_] := -((-4*I*Pi*q0 - I*w*Q0 - Sqrt[-1 +
 16*Pi^2]*w*Q0)/(2*Sqrt[-1 + 16*Pi^2]*w));
C2[Q0_, q0_, w_] := -((4*I*Pi*q0 + I*w*Q0 - Sqrt[-1 +
 16*Pi^2]*w*Q0)/(2*Sqrt[-1 + 16*Pi^2]*w));
Func[t_, Q0_, q0_, w_] := C1[Q0, q0, w]/E^((I*t*((-I)*w + Sqrt[-1 +
 16*Pi^2]*w))/(4*Pi))
 + E^((I*t*(I*w + Sqrt[-1 + 16*Pi^2]*w))/(4*Pi))*C2[Q0, q0, w];
Plot[{Func[t, Q0, q0, w1], Func[t, Q0, q0, w2]}, {t, 0, tmax},
 PlotRange -> All, AxesLabel -> {t, Q},
 PlotLegends -> {"Volume increases", "Volume decreases"}],
{{tmax, 5, "plot time (!(*SubscriptBox[(t), (max)]))"}, 0,
 20, Appearance -> "Labeled"},
{{Q0, 10, "initial condition (!(*SubscriptBox[(Q),
 (0)]))"}, 0, 100, Appearance -> "Labeled"},
{{q0, 0, "initial change rate(!(*SubscriptBox[(q),
 (0)]))"}, -10, 10, Appearance -> "Labeled"},
{{w1, 3.1415, "positive volume variation (!(*SubscriptBox[(
 [Omega]), (1)]))"}, 0, 6.2831, Appearance -> "Labeled"},
{{w2, -1.5708, "negative volume variation (!(*SubscriptBox[(
 [Omega]), (2)]))"}, -3.1415, 0, Appearance -> "Labeled"},
TrackedSymbols -> {tmax, Q0, q0, w1, w2}
]