A system executing simple harmonic motion is called a harmonic oscillator. A harmonic oscillator produces sinusoidal oscillations. The sinusoidal oscillations can be of two types. They are untamed oscillations and damped oscillations.
Untamed Oscillations
The oscillations whose amplitude remains constant with time are called untamed oscillations. A variation of amplitude with time of an untamed oscillation. Such oscillations can occur if frictional forces on the oscillating systems are absent. For example, if the bob of a simple pendulum is displaced in vacuum and then released, the bob executes simple harmonic motion with constant amplitude.
Damped Oscillation
The oscillations whose amplitude goes on decreasing with time are called damped oscillations. The variation of displacement versus time of a damped oscillation. In a real oscillating system, forces like friction are always present that dissipate the energy of the oscillator. Unless energy somehow is added to the system, dissipation eventually brings the system to rest in equilibrium.
Free Oscillations
When a body capable of oscillation is displaced from its equilibrium position and then left free, it begins to oscillate with a defined amplitude and frequency. If the body is not resisted by any kind of friction, the motion continues. Such oscillation is called the free oscillation. The frequency of vibration depends on the intrinsic properties shape, elasticity of the body which is called as the natural frequency. The force acting on the system is the restoring force. For example, when a simple pendulum is displaced from its mean position and then left free, it executes free oscillations. The natural frequency of the simple pendulum. In an absence of frictional forces, the amplitude of free oscillations would remain constant. However, in actual practice, a complete free oscillation can not be obtained in nature.
Forced Oscillations
When a body is maintained in a state of oscillation by an external periodic force of frequency other than the natural frequency of the body, the oscillation, the frequency of oscillation is equal to the frequency of the periodic force. The external applied force on the body is called the driver, and the body set into oscillations is called the driven oscillator.
Resonant Oscillations
When a body is maintained in a state of oscillations by a periodic force having the same frequency as the natural frequency of the body, the oscillations are called resonant oscillations. The phenomenon of producing resonant oscillations is called resonance. Note that the resonance is the particular case of forced oscillations in which the two frequencies are equal. If a graph is plotted between the amplitude and angular frequency of the oscillator, a curve is obtained. For examples,
a) When soldiers are passing through a bridge and their frequency of marching and natural frequency of the bridge are equal, the bridge oscillates with maximum amplitude so that the bridge may destroy. So due to this reason, the marching soldiers are ordered to break their steps while crossing a bridge.
b) A turning fork is often mounted on a sound box. The box is constructed in such a way that the natural frequency of air column inside it is the same as that of the fork. When the tuning fork is struck, it sets the air column into resonant vibrations. The reinforces the sound of the fork.
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