experiments >> the phase velocity of rope waves experiment
Coupled Pendulum
Two equal gravity pendula with a
particular characteristic frequency are coupled by a “soft” spiral spring. The amplitudes of both pendula are recorded as a function of time for various vibrational modes and different coupling factors using a y/t recorder. The coupling factors are
determined by different methods.
The related topics/experiments with this setup are as follows:
› Spiral spring
› Gravity pendulum
› Spring constant
› Torsional vibration
› Torque
› Beat
› Angular velocity
› Angular acceleration
› Characteristic frequency
For teaching purposes, the below-mentioned experiments may be carried out:
- To determine the spring constant of the coupling spring.
- To determine and to adjust the characteristic frequencies of the uncoupled pendula.
- To determine the coupling factors for various coupling-lengths using
- the apparatus constants
- the angular frequencies for “inphase” and “in opposite phase” vibration
- the angular frequencies of the beat mode.
- To check the linear relation between the square of the coupling-lengths and
- the particular frequencies of the beat mode
- the square of the frequency for “in opposite phase” vibration.
- To determine the pendulum’s characteristic frequency from the vibrational modes with coupling and to compare this with the characteristic frequency of the uncoupled pendula.
Basic features of our Pendulum system are:
- Low friction due to double bearing pendulum rod
- Sliding holder for different types of coupling
- Recording of movement over a low friction potentiometer
- Zero adjustment key
- Input voltage proportional to pendulum deflection
- Direction of deflection depends on whether voltage is positive or negative
Some related information (courtesy the WWW) is given below:
The scientist Galileo first noted (c. 1583) the constancy of a pendulum's period by comparing the movement of a swinging lamp in a Pisa cathedral with his pulse rate. The Dutch mathematician and scientist Christiaan Huygens invented a clock controlled by the motion of a pendulum in 1656. The priority of invention of the pendulum clock has been ascribed to Galileo by some authorities and to Huygens by others, but Huygens solved the essential problem of making the period of a pendulum truly constant by devising a pivot that caused the suspended body, or bob, to swing along the arc of a cycloid rather than that of a circle. The period is influenced by the position of the pendulum in relation to the Earth. Because the strength of the Earth's gravitational field is not uniform everywhere, a given pendulum swings faster, and thus has a shorter period, at low altitudes and at the Earth's Poles than it does at high altitudes and at the Equator.
Incase any query needs to be answered, please drop us an email.
experiments >> the phase velocity of rope waves experiment