have seen how we can work out the velocity at any given point by v2
)2(A2 – x2).
We also know that kinetic energy, Ek
= ˝ mv2, so it doesn’t
take a genius to see that:
m(2pf )2(A2 – x2)
can see that the maximum potential energy
is found at each end of the swing. As
the pendulum swings away from the rest position, work is done against the
restoring force. If x
= 0, the equilibrium position, the restoring force is 0 as well.
At any displacement s we can
find the restoring force F.
We can do this by using Newton II, F
= ma and a = (2pf )2x.
the force at any displacement s is
given by F = m(2pf
know that work done = force
distance moved. However the force
is not constant and we need to consider the average
force, which is half the
Work done = average force ´ displacement = ˝ m(2pf )2x ´ x = ˝ m(2pf )2x2.
we can work out the potential energy at any point using:
The total energy at any point is simply the sum of the potential and kinetic energy;
Etot = Ep + Ek
˝ m(2pf )2(A2 – x2)
+ ˝ m(2pf )2x2
= ˝ m(2pf )2A2