The motion of a particle varies with time according to the relation y = a sin ⁡ ω t + b cos ⁡ ω t

Question

The motion of a particle varies with time according to the relation y = a sin ⁡ ω t + b cos ⁡ ω t, The motion is oscillatory but not SHM, The motion is SHM with amplitude a + b, The motion is SHM with amplitude a 2 + b 2, The motion is SHM with amplitude a 2 + b 2

MARKS App · Accepted Answer

y = a sin ⁡ ω t + b cos ⁡ ω t Let a = r cos ⁡ θ a n d b = r sin ⁡ θ y = r cos ⁡ θ sin ⁡ ω t + r sin ⁡ θ cos ⁡ ω t = r sin ⁡ ( ω t + θ ) ∴ a 2 + b 2 = r 2 cos 2 ⁡ θ + sin 2 ⁡ θ = r 2 or r = a 2 + b 2

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