For particle P revolving round the centre O with radius of circular path r and angular velocity $\omega$, as shown in below figure, the projection of OP on the x-axis at time t is

(A) $x(t)=r \cos \left(\omega t+\frac{\pi}{6}\right)$

(C) $x(t)=r \sin \left(\omega t+\frac{\pi}{6}\right)$

(D) $x(t)=r \cos \left(\omega t-\frac{\pi}{6} \omega\right)$

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Elasticity & SHM

For particle P revolving round the centre O with radius of circular path r and angular velocity

ω

, as shown in below figure, the projection of OP on the x-axis at time t is

Answer: (A)

From the diagram, the particle starts at an initial angle of

3 0^{\circ} = \frac{π}{6}

radians from the positive x-axis. As it revolves with angular velocity

ω

, the angle at time t is

ω t + \frac{π}{6}

. The x-projection is given by

x (t) = r cos (ω t + \frac{π}{6})

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Single correct option