Only need problem two s@) = C sin@ + ) This clearly shows that the sum of the tw
ID: 3167351 • Letter: O
Question
Only need problem two
s@) = C sin@ + ) This clearly shows that the sum of the two oscillations is itself an oscillation: C is the amplitude of the oscillation and is a phase shift. (b) There are numbers D and , determined by A and B, such that f(0) = D cos(0 + ) Hint: use the following trigonometric identities sin( + a) = sin()cos(a) + cos() sin(a) cos(0 +a) co() cos(a) -sin() sin(a) and work backwards, successively setting the right-hand sides of (2) and (3) equal to the right-hand side of (1)] 2. In the last problem set you were asked to find the maximum amplitude of a displace- ment s(t) = Acos(N) + B sin(Nt). Show how the either of the forms (2) or (3) in Problem 1 of this set quickly leads to the answer.Explanation / Answer
2.
Divide and multiply by sqrt{A^2+B^2}
ANd set
A/sqrt{A^2+B^2}= sin(x) and , B/sqrt{A^2+B^2}= cos(x)
Hence,
s(t)=sqrt{A^2+B^2}( sin(x) cos(Nt)+ cos(x) sin(Nt))=sqrt(A^2+B^2) sin(x+Nt)
We know , sin function takes values in the interval [-1,1]
Hence the amplitude is sqrt{A^2+B^2}
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