Resonating Pendulums

The purpose of this demonstration is to teach the conditions and effects of resonance.  Our setup includes three sinkers hanging from a rod. I give credit to my colleague Alan Varella for showing me this demonstration when I first started teaching.

What I do with my class is that I would jokingly announce that I can use telekinesis to cause any sinker to oscillate at will while keeping the others still. This provides some entertainment and after I do the first demonstration, I can even challenge one of them to try to do the same or ask the class for suggestions on how the phenomenon can be repeated.

Materials

  1. 3 fishing sinkers or pendulum bobs,
  2. Some nylon string,
  3. A rod of about half a metre's length.

Procedure

  1. Tie each sinker to a piece of string of varying length and then tie the string along the rod at roughly the same distance apart.
  2. By holding the rod at one end so that the three sinkers dangle in front of your hand, you can begin to move the rod slightly and slowly at first. The hand should be moving so little that it goes unnoticed.
  3. Gradually increase the frequency of the slight hand movement and when you see the sinker with the longest line begin to start oscillating with larger amplitudes, stay at that frequency.
  4. Once you are satisfied with the oscillation of the first sinker, you can try obtaining resonance with the other two by starting over again with a higher frequency this time.

Science Explained

Resonance occurs when the frequency that you are driving the rod with is now equal to the natural frequency of the sinker on a line. Meanwhile, the other two sinkers do not oscillate as obviously as the one with the longest line.

Resonance is the tendency of a system to oscillate at larger amplitude at some frequencies than at others. A simple example will be a child on a playground swing being pushed by her friend standing at one end of the swing. If the friend pushes the child on the swing every time the swing reaches one end, more energy is being introduced each time, causing the child to swing higher and higher. Notice that a swing will always oscillate about the same frequency, with the weight of the child making little difference. At these natural frequencies of oscillation, even small periodic driving forces can produce large amplitude oscillations.

For the case of the sinker-and-line system, the frequency f at which resonance takes place for each sinker should be given by the formula

f={\frac{1}{2\pi}}\sqrt{\frac{g}{L}}

where g is the gravitational acceleration and L is the length of the line.

Hence, the pendulum with the longest string will resonate at the lowest frequency among the three.

Electroscope

An electroscope is a device that can be used to detect or measure the amount of charge in its vicinity. One of the earliest electroscopes is the gold-leaf electroscope which was invented by a British clergyman Abraham Bennet. This is a cheaper model of the leaf electroscope made using aluminum foil.

Materials

  1. Paper clip
  2. Aluminum foil
  3. Modelling clay
  4. Glass bottle with a narrow neck
  5. Steel or brass sinker

Procedure

  1. Cut two strips of aluminum foil measuring 2 cm by 0.5 cm.
  2. Straighten the paper clip before bending both ends to make two hooks. Hang the paper clip using one hook from the sinker.
  3. Pierce each aluminum strip at one end through the other hook of the paper clip, leaving it to hang from the hook.
  4. Place the paper clip and aluminum strips inside the bottle. If the sinker is smaller than the neck of the bottle, use some modeling clay to keep it in place.
  5. Now you can test the electroscope by rubbing a comb with some wool and placing it near the paper clip.

Science Explained

Negative charges (electrons) are deposited on the comb by rubbing with wool. When the comb is placed near the sinker without touching, the negative charges in the sinker are repelled. As glass is an electric insulator, the only way for them to go is downwards onto the aluminum strips. Both strips are now negatively charged and will repel each other. The extent of their repulsion is dependent on the amount of charge on the comb and its distance from the electroscope.

Oersted's Experiment

Hans Christian Oersted showed that an electric current can affect a compass needle in 1820. This confirms the direct relationship between electricity and magnetism, which in turn, paved the way for further understanding of the two. The direction of the magnetic field can be changed by flipping the wire around, which suggests that the direction of the magnetic field is dependent on the direction of current flow.

Materials

  1. 1.5V Battery
  2. Wire
  3. Compass

Procedure

  1. Place the compass on a horizontal surface.
  2. Connect the wire to both ends of the battery.
  3. Place the middle of the wire directly over the compass, parallel to the initial orientation of the needle.
  4. Observe the needle deflect to one direction.
  5. Now flip the wire over so the current flows in the opposite direction and place it over the compass again.
  6. The needle will deflect in the other direction.
  7. Additionally, you can place the compass on top of the wire now.

Science Explained

A current will carry with it its own magnetic field. The magnetic field lines form concentric circles around the wire so that the field points in one direction above the wire and the opposite direction below the wire. Using the right-hand grip rule, where one holds his hands as though he is gripping something with his thumb pointing in the direction of current flow, his fingers will curl in a way as to indicate the direction of the magnetic field. This is also the direction in which the needle deflects.