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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