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[tex]Question: $x_{1}=\frac{5}{2}[\sin (2 \pi t)+\cos (2 \pi t)], x_{2}=5\left[\sin \left(2 \pi t+\frac{\pi}{4}\right)\right]$[/tex]
Find the ratio of the amplitude of the given motion?
Options:
[tex](a) $\sqrt{2}: 1$\\(b) $2: 1$\\(c) $1: \sqrt{2}$\\(d) $1: 2$[/tex]

Respuesta :

LammettHash

Condense x₁ to get

sin(2πt) + cos(2πt) = √2 • (sin(2πt) + cos(2πt))/√2

… = √2 (cos(2πt) cos(π/4) + sin(2πt) sin(π/4))

… = √2 cos(2πt - π/4)

So the amplitude of x₁ is (5/2) • √2 = 5/√2, while the amplitude of x₂ is 5. The ratio between them is then 5/√2 : 5, or equivalently 1/√2 : 1 or 1 : √2.

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