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

Step-by-step solution

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