General Information - 3B SCIENTIFIC PHYSICS 1012844 Mode D'emploi

4. Functioning principle
The Wilberforce pendulum demonstrates cou-
pling between translation and rotation oscilla-
tions in a calibrated mass-spring system.
The cause of the coupling between the two os-
cillations lies in the geometry of the spring. A
motion along the length of the spring causes the
wire of the coil to twist, which initiates rotary
oscillation. The rotation similarly gives rise to
extension or contraction of the spring, leading to
further oscillation along its length.
For the up and down motion, the frequency of
the pendulum is influenced by both the spring
constant and the mass of the rotating body. The
period and motion of the rotary oscillation are
determined by the torsional constant of the
spring and the adjustable moment of inertia of
the rotating body.
The resonant frequency of the translation oscil-
lation can be calculated using Equation 1:
k
=
ω
trans
m
k = Spring constant
m = Mass
The resonant frequency of the rotary motion is
determined as follows:
K
=
ω
rot
J
K = Torsion constant
J = Moment of inertia of rotating body
5. Operation

5.1 General information

The following additional equipment is necessary
in order to carry out the experiments:
1 SW stand equipment set
1 SW sensors set (@230V)
or
1 SW sensors set (@115V)
1 USB oscilloscope 2x 50 MHz
1 PC, operating system Win XP, Vista, Win 7
or
1 Analogue oscilloscope 2x 30 MHz
Caution: Dynamic force sensors must not be
subjected to mechanical overloading!
• Neither dynamometer hook may be loaded
with more than 5N in the axial direction and
1 N in transverse direction.
• Be especially careful with the maximum
loading force when assembling the system
or suspending loops or springs from the
hook.
• Make sure stand rods are firmly fitted into
the base and that all other mounting ele-
ments are also firmly fitted to the stands.
5.2 Set-up for Wilberforce pendulum
• Screw the stand rods with both external and
internal threads into the outer threaded so-
ckets of the base plate.
• Extend both rods by screwing rods with ex-
ternal thread only onto the ends of them.
• Attach double clamps near the top of both
stand rods and turn them to point inwards so
that the slots are vertical and facing one an-
other.
• Remove the knurled screws from the spring
module and hook the spring onto the mount.
Tighten the nut with the rubber ring by hand
against the spring eyelet (the eyelet must
not have any play in the spring module).
(1)
(2)
1012849
Fig. 1 Spring module with coil spring
1012850
• Lay the body with hook on the cross bar and
1012851
loosely attach it from underneath with the
1017264
knurled screw.
• Hook one of the eyelets of the spring mod-
ule onto the body with hook.
1002727
• Put the dynamometer on the cross bar and
attach the second eyelet of the module to
the hook on the dynamometer.
• Carefully attach the dynamometer to the
cross bar with the knurled screw in the same
way as the body with hook. Make sure that
the red band is taut and straight.
2