a) At time period t=0
Bob A has maximum potential energy and bob B is at rest with zero energy.
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.
Bob B reaches the maximum height and its kinetic energy is converted to maximum potential energy. While bob A remains at rest.
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.
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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