List of all Variables that match an specific pattern

Question

I'd like to make a list of all constants that match an specific pattern, wich includes all terms that multiply an specific variable. For example, I'd like to take all terms that multiply t in:

(2 + 2 x) Cos[2 w t + 4 e^2 t/3 + ArcTan[2 x/s] + 2 t + 4 r/h^n]

matching this pattern: a*Cos[f + w t], and I would have:

{a,f,w}={2 + 2 x, 
         ArcTan[2 x/s] + 4 r/h^n,
         2 w+ 4 e^2 /3+2}

I tried this:

exp = (2 + 2 x) Cos[2 w t + 4 e^2 t/3 + ArcTan[2 x/s] + 2 t] //.a_ Cos[f_ + w_ t] :> {a, f, w}

output:{2 + 2 x, 4 h^-n r + (4 e^2 t)/3 + 2 t w + ArcTan[(2 x)/s], 2}

But it didn't work, since it takes only one term... This looks to work better, but still not what I want:

exp = (2 + 2 x) Cos[2 w t + 4 e^2 t/3 + ArcTan[2 x/s] + 2 t + 4 r/h^n] //.a_ Cos[f_ + w : t*(___) ..] :> {a, f, w}

output:{2 + 2 x, 4 h^-n r + ArcTan[(2 x)/s], 2 t, (4 e^2 t)/3, 2 t w}

Answer 1

expr = (2 + 2 x) Cos[2 w t + 4 e^2 t/3 + ArcTan[2 x/s] + 2 t + 4 r/h^n];

Replace[expr, 
        a_ Cos[f_ + w : Repeated[_ t]] :> {a, f, Coefficient[+w, t]}
]

(* {2 + 2 x, 
    4 h^-n r + ArcTan[(2 x)/s], 
    2 + (4 e^2)/3 + 2 w} *)

Answer 2

exp = (2 + 2 x) Cos[ 2 w t + 4 e^2 t/3 + ArcTan[2 x/s] + 2 t + 4 r/h^n];
exp /. Cos[a_] :> Cos[Collect[a, t]] /. a_ Cos[f_ + w_ t] :> {a, f, w}
(*
{2 + 2 x, 
4 h^-n r + ArcTan[(2 x)/s], 
2 + (4 e^2)/3 + 2 w}
*)