Solved: Let V be the vector space of functions that
Chapter 4, Problem 27E(choose chapter or problem)
Let V be the vector space of functions that describe the vibration of a mass–spring system. (Refer to Exercise 19 in Section 4.1.) Find a basis for V.Reference: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 form1 2 (5)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.
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