Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position, the two bobs are in constact, . One of the bobs is released after being displaced by `10^(@)` so that it collides elastically head - on with the other bob.
(a) Describe the motion of two bobs.
(b) Draw a graph showing variation in energy of either pendulum with time,for `0letle2T` , where `T` is the period of each pendulum.

Explanation

Both the pendulum are having identical bobs and lengths , So , they will execute simple harmonic motions with same time period T .
(i) At t = 0 , let us displace the bob A to the left by `10^(@)` with energy `E_(A) = E ` (potential energy ) .
` :.` Energy of bob B , `E_(B) = 0 ` .
(ii) At `t = T/4` , when bob A is releases , it strikes bob B . Bob A collides elastically with bob B . As a result , the bob A will come to rest and bob B gets velocity of A. Thus , `E_(A) = 0 ` and `E_(B) = E ` .
(iii) At ` t = (3T)/4` , bob B reaches its extreme right where its KE is converted into PE , i.e `E_(B) = E . ` Therefore , energy of bob A , `E_(A) = 0 `
where its PE is converted into KE , i.e `E_(B) = E ` . Bob B collides elastically with A and whole of its energy is transferred to bob A . Therefore , `E_(B) = 0 , E_(A) = E `
The entire cycle is thus repeated .
(b) Variation in energies f both pendulums (i.e .A and B ) with time is shown in figures (a) and (b) .