IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Resonance on Plastic Rings

## Introduction

A vibrating system has its own natural frequencies. If an external periodic force is applied on this system (apart from the restoring force) and there is some damping, the system ultimately vibrates with the frequency of the external force. The amplitude of oscillations become quite large if this external frequency is close to one of the natural frequencies. This phenomena, known as resonance, is shown in this experiment.

## Apparatus

Vibrator, Plastic ring set, function generator

Vibrator: It is made from a speaker. When a sinusoidal voltage is given to the terminals of the speaker, the diaphragm of the speaker vibrates. A stem is fixed at the center of the diaphragm which vibrates up and down together with diaphragm.

Plastic ring set: Five plastic rings (from packing materials) of different radii are joined at one place of their peripheries. This common place is fixed to the stem of the vibrator. Function generator: This is an electronic unit which generates periodic voltage. The frequency can be selected between a wide range, from few Hz to few Megahertz.

## Procedure

1. Check that the switch on the panel of the function generator is off and the amplitude knob is at minimum. The frequency selected should also be small, few Hertz.
2. Connect the output of the function generator to the speaker terminals. Switch on the function generator. Increase the voltage amplitude to maximum.
3. Increase the frequency slowly and one of the rings will suddenly start vibrating much more vigorously than the others at one particular frequency. Make finer adjustment of frequency to make this vibration stronger.
• Question: Which ring (count from outermost as 1 and then 2, 3, 4,5) has started vibrating first? Write.
• Question: What is the frequency at this time? Write in the table.
4. Slowly increase the frequency. The amplitude of vibrations of the above ring decreases significantly. But at a particular frequency the nearby ring will start vibrating. Write the ring number and frequency in the table. Play with different frequencies and get your conclusions.
5. Sometimes you may get number of nodes and antinodes on the rings. Write that also in the table.

## Discussion

Each ring has its own set of natural frequencies depending on the radius as other characteristics are same. Resonance takes place when one of the natural frequencies of a ring matches with the applied frequency. In some cases nth natural frequency of a ring may be same as \$m\$th natural frequency of another ring. In this case both rings will go into resonance. However, the number of nodes antinodes will be different for the two rings.