I have been learning oscillations this sem and found solving system of coupled oscillators a very common subject in this course.. I want to know if the procedure is always:(can be either a spring sys or pendelum system..) 1.lay down n equations for n coupled oscillators including Xn and w and k inside. such as m*X1''=k1X1 etc.. 2.find the coefficient matrix C 3.let DET(C)=0, solve for w 4.sub w back to equations in 1 and solve for Xn So, my questions is 1. is there other ways of solving such a system? 2. Is there always a solution for such a system? or under what circumstances will there be no solutions to the system? Thank you very much!