Question

A pendulum of length 28cm oscillates such that its string makes an angle of 300 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 other.
Please do answer.....

Answer 1

Angle made with vertical at extreme position= 30°

When it goes from one extreme position to the other extreme position, angle traversed = 2×30=60°

Radius = 28cm

Distance travelled = (60/360) × 2πr = 176/6 cm

Displacement = 2× r sin 30° = 2×28×1/2 = 28 cm

Distance to displacement ratio = 176/(6×28) = 22:21

Ratio is 22:21.

Answer 2

Angle made with vertical at extreme position= 30°

When it goes from one extreme position to the other extreme position, angle traversed = 2×30=60°

Radius = 28cm

Distance travelled = (60/360) × 2πr = 176/6 cm

Displacement = 2× r sin 30° = 2×28×1/2 = 28 cm

Distance to displacement ratio = 176/(6×28) = 22:21

Ratio = 22:21