Wilberforce pendulum

The Wilberforce pendulum is a combination of spring and torsion pendulum. It consists of a mass which is suspended by a long coil spring so that the coil spring is easily twisted when the mass is rotated about its vertical axis. It is a coupled pendulum, which is used in physics education as an example experiment. It was designed in 1896 by the British physicist Lionel Robert Wilberforce.

The mass of the spring can both oscillate up and down, as well as in a torsion pendulum to rotate about its vertical axis back and forth. With a particular setting shows an interesting movement in which alternately produces an exclusive rotary motion with an exclusive " up and down " vibration. The energy of the pendulum is thus alternately transferred from the translational vibration in a rotating oscillation and back to the moving slowly decays due to the attenuation.

Despite its name, the pendulum operates in a normal operation from any horizontal reciprocating movement, as is the case with the normal oscillation. On the ground are usually horizontally opposed "arms" attached to which small weights to screw to adjust the moment of inertia for the torsional vibration.

Explanation

The first surprising feature resulting from a slight coupling of the two movements, due to the geometry of the spring. If the mass is moved up and down, any downward movement leads to a slight unwinding of the spring, so that the mass undergoes a slight torque. An upward movement of the mass, however, can the number of turns of the spring rise slightly, so they wound up on, and thus gives the mass a slight torque in the opposite direction. Thus, each up and down vibration leads to a torque, which is then reflected in a light on the right and left rotation. With a pendulum swinging only up and down, so that energy is transferred from the translational vibration in the rotational vibration of each oscillation so that the amplitude of the rotational oscillation increases, and at the same time decreases the translational vibration, until the mixture after some time only performs a rotational movement.

Similarly, if the mass initially only rotates back and forth. Then performs a rotation in one direction causes the spring is wound, a rotation in the opposite direction to that being processed. Each processing thereby reducing the tensile force of the spring so that the composition can further decrease a winding can increase the tensile force as the mass moves further upward. Thus, each rotation causes the mass to more and abschwingt until energy is transmitted again from the rotation back into the translational motion and the pendulum moves only up and down.

Frequency of motion change

The pendulum can be viewed as two coupled harmonic oscillators. The motion can be described respectively as a harmonic oscillation with variable amplitude, the amplitudes oscillate in anti-phase with a sinusoidal function.

The frequency of the pendulum between the two modes of vibration changes, the difference of the natural frequencies of each vibration. The smaller the distance between these two resonant frequencies, the slower is the switching between the two waveforms. This behavior that shows all coupled pendulums, can be compared to the acoustic phenomenon of a beat with musical instruments. Where two sine tones are combined to produce a sound at a frequency equal to the difference of the individual frequencies.

For example, in a Wilberforce pendulum, in which the mass with frequency and abschwingt and rotates with a frequency of back and forth, the frequency and the relevant period is the alternate both waveforms at

Therefore, the movement changed within five seconds of a translation to the rotation and back to the translation in the next five seconds.

Usually, the moment of inertia of the mass is adjusted until the rotation frequency is very close to the translation frequency, so that the transition between the two modes of vibration is clearly visible. This is usually due to the weight and cut back on the arms possible.