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For a periodic motion represented by y=sin ω t+cos ω t, the amplitude of the motion is

Asked in JEE Main 10th April 2nd Shift 2023 · Resultant amplitude and phase

(1) √2
(2) 2
(3) 0.5
(4) 1

Answer: (1) √2

Step-by-step solution

The two terms are π/2 out of phase, so y=√1²+1² sin (ω t+π/4).

The amplitude is √2.

Why the other options are wrong

(2) Adds the two amplitudes arithmetically.
(3) Halves one of the amplitudes.
(4) Takes one term as dominant and ignores the other.

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