To compare the behavior of the system with theory you must first measure the mass m of the car and damping vane, and determine the overall spring constant k. A graph of the damping constant R as a function of magnet current is given on the next page.
1. Find the mass of the car using the laboratory scale.
2. The overall spring contant is found by measuring the displacement
of the car caused by a given force when all (4) springs are
attached. The constant k is then given by
. A pulley (a curved, frictionless, air slide) and a set of
weights are supplied for this purpose. Other methods can also be used.
3. The damping constant R vs. I has been determined for you. It is critically dependent on the width of the gap between the poles of the magnet and by how much of the vane passes through the gap. Be careful not to change the vertical height of the track, the magnet stand, or the size of the magnet air gap.
Once the essential constants are measured you should proceed to measure the amplitude of the driven oscillations of the car as a function of frequency for various values of R. Fig. 5.10 on the accompanying pages from Stephenson shows typical curves of amplitude vs. driving frequency.
The frequency of the driving mechanism can be determined from a
measurement of its period. Use the stopwatch (electronic hand timer)
to measure the time for 5-10 complete cycles of the driver. From this
you can quickly compute the frequency 
.
Measure the resonance curve (amplitude vs. driving frequency)
for at least 3 different values of R. Determine the
driving amplitude 
by measuring the total excursion of a point on the drive
string. Remember that amplitude is half the peak-to-peak value. The
driving force amplitude is 
,
where 
is approximately one-half the overall
spring constant k. Plot your experimental resonance curves and
also plot the theoretical curves on the same graph for comparison.
The theory is given by Eq. 5.40, page 132 on
the pages copied from Stephenson: use your values of the constants.
Be careful when approaching resonance that the oscillations
don't become too violent. It may be necessary to set the system at
the resonance frequency first to ascertain the allowable driving
amplitude at the lowest value of R that you are going to use. Once
is set, of course, it shouldn't be changed for the rest of the
experiment. It may not be possible to take data for low values of
the damping force for two reasons: (1) the amplitude will be too
large near resonance, and (2) the system may never settle down into
steady state motion. That is, the transient part of the behavior may
last too long.
It is possible to investigate other aspects of the system if time permits. You may wish to study the phase difference between the driving force and the position of the car. You can also study the damped, undriven oscillations as a function of R.