Procedure
and Tasks

The task of this experiment is to measure the
dispersion relation w=w(k) for a linear chain. It
serves as a preparation for the Debye specific heat experiment.

- Build
the optical
setup to register the amplitude
of a selected mass as a function of time.
- Excite
the linear chain with N=13 to oscillations.
- Register
the elongation u(t) as a function of time with Scientific Work Shop.
- Perform
the Fourier transform of u(t).
- Change
the excitation frequency (and the position) until you have all frequencies
of the system.
- Order
the resonance frequencies according to magnitude and plot them as a
function of n/N=qa/p.
(If there is a jump in the plot
reassign the numbering).
- Repeat
the experiment with N=9.
- Observe
the nodes for the different resonance frequencies.
- Include
them in the plot frequency versus n/N and draw a characteristic standing
wave.
- Fit
a theoretical curve to the experimental points.
- Derive
the effective ratio of spring constant divided by mass
- Measure
the mass of the pendulum
- Measure
the spring constant by attaching a mass of about .5 kg and measuring the
oscillation frequency
- Compare
the ratios k/m (m=mass of pendulum in linear chain) between the fit of the
dispersion relation and the individual measurements

Using Scientific Work Shop (SWS)

- Before
starting the computer the SWS-box should be turned on
- Launch
SWS
- Connect
photo-diode with input
**A**and (on PC) drag**analog plug**to**A**. - Choose
**light sensor** - Drag
**graph**to**A** - Click
sampling option, use 20Hz for Linear Chain frequencies less then 5Hz and
50 Hz for larger ones
- Click
**Monitor** - Select
optimal range on graph by double-click left scale
- To
stop and restart Monitor click
**Stop**twice (one time to change active window)

For fast Fourier transform (FFT)

- Drag
**FFT**to**A** - Click
on the right side of FFT to choose the number of sampling points: 1024
- The
frequency axis selects automatically twice the value for the sampling
frequency