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

Where ( is a constant that depends on the spring and the mass. (See the figure below.) Show that the set of all functions described in (5) (with ( fixed and c1, c2 arbitrary) is a vector space

y(t) = c1 cos wt + c2 sin wt