Slug Oscillator
simple harmonic motion - mass on spring - sine waves
What it shows:
The oscillating mass/spring system executes simple harmonic motion, and a plot of its displacement
against time results in a sine wave. Here we get lazy and let the mass itself do the graph plotting.
How it works:
We have a wooden frame with a metal cross-bar of dimensions shown in Figures 1 and 2. The mass
of 19kg and spring (k = 520kgs-2) hang from the bar. Paper (or acetate) is mounted
on a spool on one side of the frame (Fig.4). The paper leaves the spool, takes a right-angled turn over
a triangular wooden bar mounted on the frame, and over about 2m to a take-up spool mounted on
a motor driven turntable. Two pens (Fig.3) mounted at the mid-point of the mass, serve two
purposes. They of course mark out the displacement of the mass on the paper, but they also act as
pinches to control the passage of the paper as it feeds past. One pen is dark green so it is clearly
visible, the other is fluorescent yellow, invisible unless viewed under UV lighting. The mass is also
painted a fluorescent orange.
Setting it up:
Position the frame so that the paper will feed past the mass facing the audience. The take-up spool is
a wooden dowel mounted on the turntable (details of the motor turntable are in
Tools of the Trade); tape the end of the paper to this and take
up the slack. The pens are mounted on a wooden 'T' using foam tape. The 'T' slips into a hole in the
mass; the mass should then be moved along the steel rod so that the pens press against the paper.
The foam tape is a good cushion and allows the pens to flex, but the pressure on the paper is quite
critical; give it a short run to see if you have it right. The oscillating period of the mass is 1.2 seconds,
this gives a wavelength of about 15cm if you run the turntable at 2 rev s-1 or 120rpm.
Use paper of around 21cm width, this gives you an amplitude of 5cm, but if you’re worried about trees,
a standard OHP acetate roll will do; the graph isn’t as clear, and you’ll need a white backdrop such as a
screen, but it is less critical on pen pressure and is reusable if your pens are water-soluble and you don't
mind spending hours cleaning it.
Comments:
This may look incredibly ungainly, but if you get the pen pressure right, and the paper moving across
without slack, it works brilliantly. For those who didn't know, 1.47 slug = 1.47 lb ft s-2
≈ 190N ≈ 19kg. Rating ***