
These observations tell us that the v against t graph must start out at a
positive maximum, then curve down to zero, then reach a negative maximum (of
the same magnitude as the positive one) etc 

Of course, if you prefer a more mathematical sounding explanation... the
second equation is the derivative of the first and the third equation is the
derivative of the second. 

Graphs of Energy against Time 
If an oscillation is s.h.m., then the total energy possessed by the
oscillating body does not change with time. 
(Remember that an oscillation is a periodic conversion of energy
between kinetic and potential energy.) 

In practice, the total energy of most mechanical oscillations
decreases with time, usually because of air resistance or something
similar. 
An oscillation in which the total energy (and therefore the amplitude)
decreases with time is called a damped oscillation. 

Graph of Total Energy against Time 
This one is fairly easy to predict! 



Graph of Kinetic Energy against Time 
The form of this graph can be deduced by starting from the velocity against
time graph and remembering that, in general, kinetic energy is given by 

So the KE possessed by a body oscillating with s.h.m. is 



Graph of Potential Energy against Time 
Knowing that the total energy is constant, allows us to deduce that the
potential energy graph must be have the same form as the kinetic energy
graph but inverted. 

