Can you prove that the motion of centre of mass of a rope having standing waves is simple harmonic motion?

A rope between two walls has standing waves produced on it. There are 3 waves. Prove that the motion of its centre of mass for very small amplitude is simple harmonic?



I have a method but I want to check it.Can you prove that the motion of centre of mass of a rope having standing waves is simple harmonic motion?You know that you are trying to show that the force restoring the centre of mass is proportional to the displacement but in the opposite direction.

And that at small amplitudes the component of the tension that acts perpendicular to the equilibrium position ( which is the restoring force ) is directly proportional to the amplitude ( by the small angle approximation). If your proof has met these conditions then you are home and dry.

Well done ;-)

kayaks

sonic electronix