Free, forced Vibrations and Resonance

Body oscillating with its natural frequency possesses free oscillations since no external force is there. A vibrating body would continue to vibrate forever, if there were no resistive forces present in the nature. The motion in which the amplitude of vibration remains constant with time is known as un damped oscillatory motion.

When a pendulum is displaced from its equilibrium position and released, it oscillates with its natural frequency. But its motion dies out eventually due to the air drag and force of friction opposing its motion. The pendulum, in this case, is said to execute damped oscillations. However, an external agency can maintain these oscillations. In this case, the oscillations are called forced or driven oscillations. Amplitude resonance is the state of forced vibrations in which the amplitude reaches a maximum value.

When the driving frequency is close to the natural frequency, there is an increase in amplitude of the body. This phenomenon is known as resonance. At resonance, amplitude of vibrations is very large as the body absorbs maximum energy from the impressed source. Examples of resonance are vibrations of simple pendulum with one another, tuning fork with sonometer, tuning fork and an air column, rhythm of feet of soldiers and bridge.

Coupled oscillations are the oscillations between two bodies in contact such that one body is not of infinite mass. Time period of two bodies is coupled to each other.  

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