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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 cosωt+c2 sinωt where ωis 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 ωfixed and c1, c2 arbitrary) is a vector space. | Numerade
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