For particle P revolving round the centre O with radius of circular path r and regular velocity a, as shown in below figure, the projection of OP on the x-axis at time t is
Text Solution
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As can be seen from the diagram, the initial phase of the particle is given by
=30°
The equation of motion of the particle at its initial position at time t = 0 can be written as
x(t)=rcos 
...
where, 
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 
...
Substitute the values to the known parameters into equation to obtain the required expression
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