If a mass m is placed at the end of a spring and if the

Question

Question: 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) = c₁ cos ωt + c₂ sin ωt

Where ω 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 ω fixed and c1, c2 arbitrary) is a vector space.