(a) A water molecule consists of two hydrogen atoms connected at an angle of 105o to an oxygen atom whose relative mass is 16 times that of the hydrogen atoms. If the bonds are modeled as linear unit springs, determine the fundamental frequencies and describe the corresponding vibrational modes.
(b) Do the same for a carbon tetrachloride molecule, in which the chlorine atoms, with atomic weight 35, are positioned on the vertices of a regular tetrahedron and the carbon atom, with atomic weight 12, is at the center.
(c) Finally try a benzene molecule, consisting of 6 carbon atoms arranged in a regular hexagon. In this case, every other bond is double strength because two electrons are shared. (Ignore the six extra hydrogen atoms for simplicity.)