Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is..........

Figure shows the circular motion of a particle. The radius of the circ

1.	Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is..........
Answer» `x (t) = B SIN ((2pi t)/(30))` `x (t) = B cos ((pi t)/(15))` `x (t) = B sin ((pi t)/(15)+(pi)/(2))` `x (t) = B cos ((pi t)/(15)+(pi)/(2))` Solution :Suppose a particle is MOVING uniformly on a circle of RADIUS r with ANGULAR speed `omega` and when it is on point Q it makes an angle `theta` as shown in figure. Here `theta = omega t` In right triangle `triangleORQ` `sin theta = (OR)/(OQ)` `OR = OQ sin theta` `=r sin omega t"[Radius of circle OQ = r and " theta = omega t]` OR is the X-component `therefore x(t) = B sin ((2pi)/(T)t)""[therefore r= B, omega = (2pi)/(T)]` `therefore x(t) = B sin ((2pi)/(30)t)`.