Let V be the vector space of functions that describe the vibration of a mass–spring system. (Refer to Exercise 19) Find a basis for V .

Data from in Exercise 19

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 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.

Transcribed Image Text:

y(t) = C₁ coswt + C₂ sin wt