Nonlinear parameter identification of ODE

Currently, I'm working on a mathematical model of bridge dynamics as a research project. I have successfully obtained the bridge parameters in non-dimensional form which is an ODE as shown below;

x''+ax'+bx+cx^3=F(t)

where a and b are known values, F as the forcing function and c being the nonlinear parameter. I would like to know if anyone can kindly suggest me a method to estimate the value of c? I've been stuck for a really long time now.

Thank you.