Consider a swing whose one end is fixed above the other rope by ''b'. The distance between the poles of swing is `a`. The lengths `l_(1)` and `l_(2)` are such that `l_(1)^(2) +l_(2)^(2) =a^(2) +b^(2)` as shown. The period of the smaller oscillations of the swing, by neglecting the height of the swinging person, is.....

Answer

A, B

Explanation

Given `a^(2) + b^(2) = l_1^(2) + l_(2^(2))`
`tan theta = (b)/(a)`
`tan alpha = (l_(2))/(l_(1))`
Let `OT = x_(1), TQ = x_(1), PT = d TS = y`
From geometry
`d + y = l_(1) sin (alpha + beta)`
and `d + l_(1) cos (alpha + theta) tan theta = l_(1) sin (alpha + theta)`
`rArr d = (l_(1) l_(2))/(a) :. T = 2pisqrt((d)/(g)) = 2pisqrt((l_(1)l_(2))/(ag))`