Please explain in detail how to solve this problem: A pendulum of length 28cm oscillates such that its string makes an angle of 30 degrees from the vertical when it is at one of the extreme positions. Find the ratio of the distance to displacement of the bob of the pendulum when it moves from one extreme position to the other.

In the above figure angle C'OA = 30 degree = Π/6 radian = Φ ,( say)

                                            = angle C'OB

where B is other extreme position.

Now displacement from A to B = straight line AC'B

and distance from A to B = arc ACB.

 

Putting Φ = Π/6 we get

 

ratio = (Π/6)/(sinΠ/6)

       =(Π/6)/(1/2)

       = Π/3