Welcome to practical physicsPracticle physics - practical activities designed for use in the classroom with 11 to 19 year olds
 

Barton’s pendulums

Demonstration

Students look along a line of coupled pendulums, of different lengths, and observe how they behave when a driver pendulum starts oscillating.

Apparatus and materials

  • video camera & support
  • slide projector or other suitable light source

Materials for constructing the pendulums and support, as shown in diagram.

  • AB wooden support, horizontal, 1.5 m long
  • H, H screw eyes or nails
  • T thin string or thread
  • D driver, mass about 0.04 kg
  • N nylon fishing line
  • C paper cones; cut 60 mm diameter circles from stiff white paper and then, after cutting along a radius, slide the exposed radial edges round until a cone of double thickness of paper is formed; 'fix' the cone using glue.
  • plastic curtain rings 20 mm, one per cone

Health & Safety and Technical notes



This diagram shows how to construct the demonstration apparatus.

Firmly clamp the wooden support rod so as to leave an unobstructed view along the line of pendulums. The lengths of the pendulums can be from about 0.25 m to 0.75 m with the driver pendulum 0.5 m long.

The cone pendulums may be attached to the cross string, T, by a half-hitch or slip-knot; this makes it easy to adjust the lengths. Position the pendulums as close together as possible. An alternative is to use thread instead of nylon line, securing each cone pendulum to the cross string with a blob of Plasticine at the end of its thread.

The damping of the cone pendulums can be reduced by slipping plastic curtain rings over the cones. This is easily done if the rings have been cut in advance.

The demonstration is most effective in a darkened room with the cones illuminated by a bright light source.

Procedure


1 Arrange students so that they are looking along the line of pendulums.

2 Displace the driver pendulum quite far from its equilibrium position and then release it. 

3 Carefully observe what happens to the coupled pendulums. Help students to see resonance, phase relationships, transient oscillations and damping effects. Note which cone pendulum is in resonance with the driver.

Teaching notes


a Help students link the behaviour of this system to other experiments involving resonance that they may have done.

b Any resonant system behaves as follows.
i When a driving force (driver) acts on something which can vibrate, the initial transient oscillations are irregular, with varying amplitude.

ii These transient oscillations give way, in a time which depends on the degree of damping, to a steady state, in which the driven oscillator oscillates at the forcing frequency, regardless of its own natural frequency. (Damping is the result of friction-type forces which always act against the motion of an oscillator.)

iii The amplitude of the driven oscillation depends on the forcing frequency and rises to a maximum if the forcing frequency is equal to the natural frequency of the driven oscillator. These large amplitude vibrations are called resonant oscillations. See the sketch graph below.

iv At resonance the driver and the driven oscillator are not in phase.
The driver leads by one quarter of a cycle.

c Photograph (c) below shows Barton's pendulums instantaneously when the driver was at its maximum displacement to the left. The resonating pendulum is just passing through the centre of its oscillation, and moving to the left. It is one quarter of a cycle, or p /2, behind the driver. The shorter pendulums at the top of the picture, with higher natural frequency, are moving approximately in phase with the driver.

The long pendulums with lower natural frequencies, are approximately in antiphase with the driver (phase difference of p). Notice how the pendulums which have natural frequencies close to the forcing frequency (that is, pendulums of similar length to the driver), oscillate with larger amplitude than the others.
The amplitude of the forced vibrations also depends on the degree of damping. Photographs (a) and (b) illustrate how the amplitude of resonant vibrations is reduced by damping.

This experiment has yet to undergo a health and safety check.

Related guidance


Resonance

Energy in forced oscillations

 

Related experiments


Forced vibrations of a mass on a string

Resonance of a pendulum

Hacksaw blade resonance

 

 

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