sol={-k x[t]+l m2 Sin[[Theta][t]] ([Theta]^[Prime])[t]^2-(m1+m2) (x^[Prime][Prime])[t]-l m2 Cos[[Theta][t]] ([Theta]^[Prime][Prime])[t]==0,-l m2 (g Sin[[Theta][t]]+Cos[[Theta][t]] (x^[Prime][Prime])[t]+l ([Theta]^[Prime][Prime])[t])==0}

Cases[sol,Derivative[2][x][t]]

{}

Position[sol,Derivative[2][x][t]]

{{1, 1, 3, 3}, {2, 1, 4, 2, 2}}

sol[[2, 1, 4, 2, 2]](*x''[t]*)
sol[[1, 1, 3, 3]](*x''[t]*)

HoldForm[MatrixForm[{F,T}]==MatrixForm[MatrixForm[{{m1+m2,m2 l Cos[[Theta][t]]},{m2  l Cos[[Theta][t]],m2 l^2}}].MatrixForm[{x''[t],[Theta]''[t]}]]+MatrixForm[{{0,-m2 l Sin[[Theta][t]]},{0,0}}].MatrixForm[{x'[t]^2,[Theta]'[t]^2}]+MatrixForm[{k x[t],m2 g l Sin[[Theta][t]]}]]