Proving that a value does not decay in the process of motion

Question

Hi

 

How do I go about proving that a value for energy does not decay during the process of motion? 

 

Thanks

 

 

Answer 1

I suggest trying to show that

dE/dt = 0

That would demonstrate that E is conserved. It looks like you have a sum of kinetic and potential energy, so you would have to prove that the time rate of change of the kinetic energy is the negative of the time rate of change of the potential energy. But that means you will need explicit functions for y(t) and V(x(t)) to differentiate.