### Three pendulums

What you can do here
Try to make the pendulums oscillate by rhythmically pulling the rope (in sequence for about one second on each side). Only a certain frequency (different for every pendulum) can make them swing with a large amplitude. Getting all the three pendulums to swing with a large amplitude simultaneously is impossible. Note that the greater the pendulum length (the longer the ropes which the ball is suspended from), the longer the oscillation period, meaning you need to pull the rope less often to set the pendulum swinging.

How it works

If pendulum oscillations have a small amplitude, they may be approximated as harmonic oscillations. Harmonic oscillations occur when a force directly proportional to the displacement acts on a physical body in the opposite direction to that of displacement. Each of the pendulums has a different natural period i.e. the time of one ”full swing” after it is displaced from the equilibrium and allowed to move freely. Each pendulum also has a different natural frequency (reciprocity of the natural period). The longer the pendulum, the longer the natural period and the lower the natural frequency. When you pull the rope with the same frequency as the natural frequency of a given pendulum (when the driving frequency is equal to the natural frequency), resonance occurs and the amplitude of pendulum oscillations may reach its maximum. The frequency for which the amplitude of oscillations is at its maximum is called the resonance frequency. Each pendulum has a different length, thus a different driving frequency is needed to oscillate it with a large amplitude. It is impossible for all three pendulums at the same time.

Interesting facts

Bridge engineers need to bear resonance in mind. On 7 November 1940 in Tacoma (USA), the 850-metre-long (2,800-feet-long) main span of a suspension bridge collapsed just four months after it first opened. The strong wind of 64 km per hour (40 miles per hour) made it vibrate and destroyed it. The event was filmed and it may be easily found on the Internet.