ClearAll["Global`*"]
m={{2,0},{0,1}}*2500;
k={{3,-1},{-1,1}}*20000 Pi^2;
w1=N[2Pi,5];
w2=6.2832;
D1=Det[k-w1^2*m]
D2=Det[k-w2^2*m]

ClearAll["Global`*"]
m={{2,0},{0,1}}*2500;
k={{3,-1},{-1,1}}*20000 Pi^2;
w1=N[2Pi,5];
w2=2Pi;
D1=Det[k-w1^2*m]
D2=Det[k-w2^2*m]

w1 == 2 [Pi]
(* True *)
w1 - w2
(* -0.0000146928 *)

Plot[Det[k - w^2*m], {w, 6.2831, 6.2833}]