Periodic and Oscillatory (Vibratory) Motion
Category : JEE Main & Advanced
(1) A motion, which repeat itself over and over again after a regular interval of time is called a periodic motion.
Revolution of earth around the sun (period one year), rotation of earth about its polar axis (period one day), Motion of hour's hand of a clock (period 12-hour) etc are common example of periodic motion.
(2) Oscillatory or vibratory motion is that motion in which a body moves to and fro or back and forth repeatedly about a fixed point in a definite interval of time. In such a motion, the body is confined with in well-defined limits on either side of mean position.
Oscillatory motion is also called as harmonic motion.
(i) Common examples are
(a) The motion of the pendulum of a wall clock
(b) The motion of a load attached to a spring, when it is pulled and then released.
(c) The motion of liquid contained in U-tube when it is compressed once in one limb and left to itself.
(d) A loaded piece of wood floating over the surface of a liquid when pressed down and then released executes oscillatory motion.
(ii) Harmonic oscillation is that oscillation which can be expressed in terms of single harmonic function (i.e. sine or cosine function). Example : \[y=a\sin \omega \,t\] or \[y=a\cos \omega \,t\]
(iii) Non-harmonic oscillation is that oscillation which can not be expressed in terms of single harmonic function. It is a combination of two or more than two harmonic oscillations. Example : \[y=a\sin \omega \,t+b\sin 2\omega \,t\]
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