If a mass m is placed at the end of a spring, and if the mass is pulled downward and released, the mass-spring system will begin to oscillate. the displacement y of the mass from its resting position is given by a function of the form y(t)equalsc 1 cosine omega t plus c 2 sine omega t, where omega is a constant that depends on the spring and the mass. show that the set of all functions of this form (with omega fixed and c 1 and c 2 arbitrary) is a vector space.