We have a damped harmonic oscillator demo. The damping is not
really of the viscous form but simply is a constant kinetic frictional
force. The result is a slightly modified envelope decay function.
We shall neglect this and imagine that our system indeed displays
exponential decay. We wish to determine the life-time, 
,
and the difference between 
and 
.
We readily measure 
by timing the undamped
system. To determine we measure 
the time
taken to halve the amplitude of oscillation. It is related to by
We can now determine the modified resonance frequency by
It can be hard to see directly the shift in the resonance frequency
brought about by friction in this experiment since
by definition it is small if we are looking at a weakly damped system.