Answer :

a) At time period t=0


Bob A has maximum potential energy and bob B is at rest with zero energy.


At t=T/4


Bob A gains maximum velocity and collides with the bob B. bob A comes to rest and bob B gains the velocity of bob A because the collision is elastic and both have the same mass their velocity gets interchanged.


Now bob B has maximum kinetic energy.


At t=T/2


Bob B reaches the maximum height and its kinetic energy is converted to maximum potential energy. While bob A remains at rest.


At =3T/4


Bob B reaches to bob A with its maximum potential energy getting converted to max kinetic energy and collides with bob A. During the collision the interchanging of velocity takes place and bob A gains the velocity of bob B and bob B comes to rest.


At t=T


Bob A reaches the maximum height and its kinetic energy is converted to maximum potential energy. While bob B remains at rest.


And after t=T the whole process between 0<t<T repeats itself in the time period of T<t<2T


b) Here E is total energy of bob A and B we get straight lines, since they E is constant.


Now from the above discussion in part a) we get the following graphs,


For bob A,



For bob B,



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