Kinda weird when in the final stretch you decided to add the values you had calculated for A and B instead of recalling the first equation that said that A + B = x_0
Yes, they are all solutions to the same differential equation. You can show that the e^iwt version is the same as sin and cosine version using the Euler equation. Maybe I'll make an update.
amazing explanation , question: in 2nd equation why did you select A(cos wt + phi) why not A(sin wt + phi) and both equations will give negative sign in X double dot?? , why use COS instead of SIN
to the best of my knowledge I think you can use either, but it will change the phi value, as the sin and cosine standard functions we are used to are the same if shifted by pi radians.
