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

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As can be seen from the diagram, the initial phase of the particle is given by
$\begin{array}{rcl} φ & = & 30 ° \\ = & \frac{π}{6} \end{array}$
The equation of motion of the particle at its initial position at time $t = 0$ can be written as
$x (t) = r \cos θ . . . (1)$
where, $θ$ is the angular displacement of the particle at time $t = t$ .
Since, the position of the particle at a later instant of time always lags behind its initial position at time $t = 0$ , the equation of motion of the particle at any instant of time is given by
$x (t) = r \cos (θ + φ) . . . (2)$
Substitute the values of the known parameters into equation (2) to obtain the required expression
$x (t) = r \cos (ω t + \frac{π}{6})$

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