For a periodic motion represented by the equation The amplitude of the motion is [2023]

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Solution

Q.
For a periodic motion represented by the equation $Y = \sin ω t + \cos ω t$

The amplitude of the motion is [2023]

1 $0.5$

2 $\sqrt{2}$

3 $1$

4 $2$

Ans.
(2)

$y = \sin ω t + \cos ω t$

$y = \sin ω t + \sin (ω t + \frac{π}{2})$

$Δ ϕ = \frac{π}{2}$

$A_{net} = \sqrt{1^{2} + 1^{2} + 2 \times 1 \times 1 \times \cos (Δ ϕ)}$

$A_{net} = \sqrt{2}$

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