Every body will have some frequency with which it vibrates and it is called its natural frequency.Under the influence of external force body vibrates with a frequency different from its natural frequency and it is called forced vibration. Resonance is a special case of forced vibration.If the frequency of external force is equal to the frequency of body which is going to be vibrated then the body virates with the maximum frequency and the phenomenon is called Resonance.
A person swinging in a swing without anyone pushing it or a simple pendulum, displaced and released, are examples of free oscillations. In both the cases, the amplitude of swing will gradually decrease and the system would, ultimately, come to a halt. Because of the ever present dissipative forces, the free oscillations cannot be sustained in practice.
However, while swinging in a swing if you apply a push periodically by pressing your feet against the ground, you find that not only the oscillations can now be maintained but the amplitude can also be increased. Under this condition the swing has forced, or driven, oscillations.
The maximum possible amplitude for a given driving frequency is governed by the driving frequency and the damping, and is never infinity. The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the oscillator is called resonance.
Example for Resonance
Consider a set of five simple pendulums of assorted lengths suspended from a common rope as shown in figure. The pendulums 1 and 4 have the same lengths and the others have different lengths. Now let us set pendulum 1 into motion. The energy from this pendulum gets transferred to other pendulums through the connecting rope and they start oscillating. The driving force is provided through the connecting rope. The frequency of this force is the frequency with which pendulum 1 oscillates. If we observe the response of pendulums 2, 3 and 5, they first start oscillating with their natural frequencies of oscillations and different amplitudes, but this motion is gradually damped and not sustained.
Their frequencies of oscillation gradually change and ultimately they oscillate with the frequency of pendulum 1, i.e. the frequency of the driving force but with different amplitudes. They oscillate with small amplitudes. The response of pendulum 4 is in contrast to this set of pendulums. It oscillates with the same frequency as that of pendulum 1 and its amplitude gradually picks up and becomes very large. A resonance-like response is seen. This happens because in this the condition for resonance is satisfied, i.e. the natural frequency of the system coincides with that of the driving force.
SHM related topics
Damped simple harmonic motion
Simple Pendulum
What is periodic and Oscillatory Motion is ? Displacement in Oscillatory motion
Simple Harmonic Motion
Velocity and acceleration of SHM
Energy of particle in SHM
Wave Motion an introduction
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