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.