of the Earth around the Sun, waxing and waning of Moon, etc. . Non-Periodic motion Any motion which does not repeat itself after a regular interval of time is known as non-periodic motion. Example : Occurance of Earth quake, eruption of volcano, etc.
EXAMPLE . Classify the following motions as periodic and non-periodic motions?. a. Motion of Halley’s comet.
b. Motion of clouds. c. Moon revolving around the Earth.
Solution a. Periodic motion Figure . . Oscillatory or vibratory motions - - - - Unit Oscillations Simple harmonic motion is a special type of oscillatory motion in which the acceleration or force on the particle is directly proportional to its displacement from a fixed point and is always directed towards that fixed point.
In one dimensional case, let x be the displacement of the particle and a x be the acceleration of the particle, then a x ∝ x ( . ) a x = − b x ( . ) where b is a constant which measures acceleration per unit displacement and dimensionally it is equal to T − . By multiplying by mass of the particle on both sides of equation ( .
) and from Newton’s second law, the force is F x = − k x ( . ) where k is a force constant which is defined as force per unit length. The negative sign indicates that displacement and force (or acceleration) are in opposite directions. This means that when the displacement of the particle is taken towards right of equilibrium position ( x takes positive value), the force (or acceleration) will point towards equilibrium (towards left) and similarly, when the Figure .
Oscillatory or vibratory motions . SIMPLE HARMONIC MOTION (SHM) Figure . Simple Harmonic Motion