When the displacement is maximum, the particle is momentarily at rest, which means that at this point (assuming no friction present) all the mechanical energy is elastic potential, which can be written as follows:
Since in absence of friction, total mechanical energy must keep constant, this means that at any time, the sum of the kinetic and potential energy, must be equal to (1), as follows:
If KEf = U/2f, replacing in (2), we get:
At any point, the elastic potential energy is given by the following expression:
where k= spring constant (N/m) and x is the displacement from the
equilibrium position.
Replacing (4) in (3), simplifying and rearranging, we get:
There will not be enough momentum from the first hill to cross another hill if he same or larger size because of the way potential energy and kinetic energy works it will not be able go as high as it could go on he fist hill.
