For a periodic motion represented by the equation $\mathrm{Y}=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$ The amplitude of the motion is

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Elasticity & SHM

For a periodic motion represented by the equation

Y = sin ω t + cos ω t

The amplitude of the motion is

Answer: (B)

Rewrite

y = sin ω t + cos ω t

y = sin ω t + sin (ω t + \frac{π}{2})

. These are two SHMs with the same amplitude (1) and phase difference

Δ ϕ = \frac{π}{2}

. The resultant amplitude is

A_{net} = 1^{2} + 1^{2} + 2 (1) (1) cos (\frac{π}{2}) = 2

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option