Page 1 :
Periodic Motion, , A motion which repeats itself identically after, a fixed interval of time is called periodic, motion. e.g., orbital motion of the earth, around the sun, motion of arms of a clock,, motion of a simple pendulum etc., , Oscillatory Motion, , A periodic motion taking place to and fro or, back and forth about a fixed point, is called, oscillatory motion, e.g., motion of a simple, pendulum, motion of a loaded spring etc., , Note Every oscillatory motion is periodic, motion but every periodic motion is not, oscillatory motion., , Harmonic Oscillation, , The oscillation which can be expressed in, terms of single harmonic function, i.e., sine or, cosine function, is called harmonic, oscillation.

Page 2 :
Simple Harmonic Motion, , A harmonic oscillation of constant amplitude, and of single frequency under a restoring, force whose magnitude is proportional to the, displacement and always acts towards mean, Position is called Simple Harmonic Motion, (SHM)., , , , A simple harmonic oscillation can be, expressed as, , y=asin wt, ory=acos wt, , Where a = amplitude of oscillation.

Page 3 :
Non-harmonic Oscillation, , Anon-harmonic oscillation is a combination, of two or more than two harmonic, oscillations., , It can be expressed as y=asin wt+bsin 2wt, Some Terms Related to SHM, , (i) Time Period Time taken by the body to, complete one oscillation is Known as time, period. It is denoted by T., , (ii) Frequency The number of oscillations, completed by the body in one second is, called frequency. It is denoted by v., , Its SI unit is ‘hertz’ or ‘second-"’., Frequency = 1/ Time period, , (iii) Angular Frequency The product of, frequency with factor 211 is called angular, frequency. It is denoted by w., , Angular frequency (W) = 2TIv, , Its SI unit is ‘hertz’ or ‘second-".

Page 4 :
(iv) Displacement A physical quantity which, changes uniformly with time in a periodic, motion. is called displacement. It is denoted, , by y., , (v) Amplitude The maximum displacement in, any direction from mean position is called, amplitude. It is denoted by a.

Page 5 :
(vi) Phase A physical quantity which express, the position and direction of motion of an, oscillating particle, is called phase. It is, denoted by g., , Simple harmonic motion is defined as the, projection of a uniform circular motion on, any diameter of a circle of reference., , Some Important Formulae of SHM, , (i) Displacement in SHM at any instant is, given by, , y=asin wt, , or y=acos wt, , where a = amplitude and, W = angular frequency., , (ii) Velocity of a particle executing SHM at any, instant is given by, , V = W v(a2 - y2), At mean position y = 0 and vis maximum, , Vmax = AW