q[t_,ω_,α_]:=Exp[-α t]Cos[ω t];
Manipulate[Plot[{q[t,ω,α],q[t,0,α]},{t,0,10},PlotRange->{-1,1},
PlotStyle->{Thickness[0.005]}],{{α,0},0,10,0.01},{{ω,2 π/4},0,10,0.01}]

Plot[{ArcTan[x],Pi/2,-Pi/2},{x,-10,10},PlotRange->{-Pi/2,Pi/2}]

Io[R_,L_,C_,ω_,ϵo_]:=ϵo*((((R^2)+(((ω L - 1/(ω C)))^2)))^(-1/2));
ϵo=1;
Manipulate[Plot[{Io[R,L,C,ω,ϵo]},{ω,0,10},PlotRange->{0,5}],
{{R,1},0,1,0.01},
{{L,1},0,10,0.01},
{{C,1},0,10,0.01}]

Io[R_,L_,C_,ω_,ϵo_]:=ϵo*((((R^2)+(((ω L - 1/(ω C)))^2)))^(-1/2));
ϕ[R_,L_,C_,ω_,ϵo_]:=ArcTan[-(1/R)(ω L - (1/(ω C)))];
ϵo=1;
Manipulate[{Plot[{Io[R,L,C,ω,ϵo]},{ω,0,10},PlotRange->{0,5}],
Plot[{ϕ[R,L,C,ω,ϵo]},{ω,0,5},PlotRange->{-Pi/2,Pi/2}]},
{{R,1},0,1,0.01},
{{L,1},0,10,0.01},
{{C,1},0,10,0.01}]

Io[R_,L_,ωo_,ω_]:=1*((((R^2)+(((L/ω))^2)((((ω^2)-((ωo)^2)))^2)))^(-1/2));
ϕ[R_,L_,ωo_,ω_]:=ArcTan[-(L/(R ω))((ω^2)-((ωo)^2))];
ϵo=1;
Manipulate[{Plot[{Io[R,L,ωo,ω]},{ω,0,10},PlotRange->{0,5}],
Plot[{ϕ[R,L,ωo,ω]},{ω,0,10},PlotRange->{-Pi/2,Pi/2}]},
{{R,1},0,1,0.01},
{{L,1},0,10,0.01},
{{ωo,1},0,10,0.01}]