I am tasked to answer the following question on the subject of coupled pendulums: QUESTION: The Antisymmetric and symmetric normal modes can be superposed to obtain new solutions. Can ANY solutions be written as a superposition of these two modes? Justify your answer. Hint: Is a solution completely characterised by its initial positions and velocities? My answer: I say yes any solution can be written as a superposition of these two modes as it's a consequence of linearity of the system (It's a linear system because restoring force is linearly proportional to the displacement from equillibrium). If the antisymmetric and symmetric modes are each a solution, then any linear combination of those is also a solution. What do you guys think? Is that wrong?