Question: How do I calcuate the residue of this expression?

I would like to calcuate the residue of the following expression that I call res

>res:= subs([S1 = C3-sqrt(C3^2+4*C1*s), S2 = C3+sqrt(C3^2+4*C1*s)], exp(s*t)*(S1*(sinh((1/2)*S1)-cosh((1/2)*S1))*(sinh((1/2)*S2*eta)-cosh((1/2)*S2*eta))-S2*(sinh((1/2)*S2)-cosh((1/2)*S2))*(sinh((1/2)*S1*eta)-cosh((1/2)*S1*eta)))*exp(C4)/((S2*(sinh((1/2)*S2)-cosh((1/2)*S2))-S1*(sinh((1/2)*S1)-cosh((1/2)*S1)))*C1*s^2)):

To do this I first want to find the roots (poles) of the demnom of the expression. (equal to zero as below)

> resdenom := denom(res):

>sol:=solve(resdenom,s)

But I then get the RootOf expression , but the Rootof expression is unmathematical analytical expression.How to solve the residue of the res?

Please help me in anyway you can as I am completely stuck.