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Okay, I just took the final for my first DE class! I really liked it, now I can actually know how to derive some of these equations that they just hand to you in physics and chemistry.

So anyway, there is the solution to the angular position(from vertical)of the simple pendulum; the one example we had from class(physics) was theta(t)=Theta-max[e^(-bt/2m)], but i think that the cos(omega*t+phase change) part was ommited?

So I am really interested in deriving this! So I know the motion of the pendulum is given by the diffy Q I(alpha)+b(omega)+g(theta)/L=0 where sin theta has been replace by theta because of small angle approximation, and omega and alpha are the 1st and 2nd derivatives of theta(t). So then what?. Do I solve the aux eq r^2I +rb+g/L or what? Am I on the right track?

This is for my own curiosity only, Uhh please don't tell me to "go study my book a little better" heh heh. Hell even my physics prof. would flounder trying to explain, and dudes got a doctoral degree! Like I said, we are not expected to derive these, but enquiring minds want to know! Thanks

So anyway, there is the solution to the angular position(from vertical)of the simple pendulum; the one example we had from class(physics) was theta(t)=Theta-max[e^(-bt/2m)], but i think that the cos(omega*t+phase change) part was ommited?

So I am really interested in deriving this! So I know the motion of the pendulum is given by the diffy Q I(alpha)+b(omega)+g(theta)/L=0 where sin theta has been replace by theta because of small angle approximation, and omega and alpha are the 1st and 2nd derivatives of theta(t). So then what?. Do I solve the aux eq r^2I +rb+g/L or what? Am I on the right track?

This is for my own curiosity only, Uhh please don't tell me to "go study my book a little better" heh heh. Hell even my physics prof. would flounder trying to explain, and dudes got a doctoral degree! Like I said, we are not expected to derive these, but enquiring minds want to know! Thanks

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