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 wt + c₂ sin ot, where is a constant that depends on the spring and the mass. Show that the set of all functions of this form (with fixed and c₁ and ₂ arbitrary) is a vector space. Theorem: If V₁....,V, are in a vector space V, then Span{V₁Vp} Let H be the set of all functions described by y(t) = c₁ cos at + c₂ sin @t. In order to apply the theorem, what must be shown? sa subspace of V. OA. That H can be written as a sum of vectors from a vector space V O B. That H can be written as the span of vectors from a vector space V O C. That H can be written as a set of vectors from a vector space V O D. That H can be written as scalar multiples of a single vector from a vector space V 囂 H wwwwwwwwwww.
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 wt + c₂ sin ot, where is a constant that depends on the spring and the mass. Show that the set of all functions of this form (with fixed and c₁ and ₂ arbitrary) is a vector space. Theorem: If V₁....,V, are in a vector space V, then Span{V₁Vp} Let H be the set of all functions described by y(t) = c₁ cos at + c₂ sin @t. In order to apply the theorem, what must be shown? sa subspace of V. OA. That H can be written as a sum of vectors from a vector space V O B. That H can be written as the span of vectors from a vector space V O C. That H can be written as a set of vectors from a vector space V O D. That H can be written as scalar multiples of a single vector from a vector space V 囂 H wwwwwwwwwww.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 wt + C₂ sin wt, where w is a constant that depends
on the spring and the mass. Show that the set of all functions of this form (with a fixed and c₁ and c₂ arbitrary) is a vector space.
V are in a vector space V, then Span {V1₁,...,\
Vp) is a subspace of V.
р
Let H be the set of all functions described by y(t) = C₁ cos wt + C₂ sin ot. In order to apply the theorem, what must be shown?
Theorem: If v₁
A. That H can be written as a sum of vectors from a vector space V
B. That H can be written as the span of vectors from a vector space V
C. That H can be written as a set of vectors from a vector space V
O D. That H can be written as scalar multiples of a single vector from a vector space V
wwwwww
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