Question

A pendulum of length 28 cm oscillates such that it's string makes an angle of 30° from the vertical when it is at one of the extreme position . Find the ratio of the distance to displacement of the bob of pendulum when it moves from one extreme position to other

Answer 1

let A be the first extreme position and C be the second position when pendulum starts from points B

length of pendulum,   OB = 28 Cm

Thus radius of Arc formed = 28 Cm

length of arc for first extreme,      AB = pi/6 * OA
                                                     AB = 14.65 Cm
and                 Thus                      BC = 14.65  Cm

Thus distance =    AB + BC
                       =     14.65+14.65
                      =     29.30 Cm

now Join A and C such that D is point on Line OB

thus                              Sin 30 deg = AD/28
                                                   AD = 14 Cm

thus   displacement   = 2 * AD
                                   = 2 * 14
                                   = 28 Cm

ratio = 29.30/ 28