o Simple harmonic motion is an example of periodic oscillatory motion. O Special type of oscillatory motion which satisfies following conditions. A. Oscillatory amplitude of particle is small. B. During oscillation, acceleration towards mean position, due to net restoring force, is directly proportion to displacement from mean position. Force displacement relation in S.H.M. F = -ky, where K is force constant (Force law in S.H.M.), yis displacement from mean position. o Acceleration of particle K a = m y =- wy m -A +A . Acceleration and displacement are antiparallel d'y dt? + ofy = 0, here o=, K (Angular frequency) mis mass oscillating, Kis force constant. General equation for displacement in S.H.M. y= A sin (ot + ) or y= A cos (ot t) = 2rn is angular frequency and (ot + ) is called phase, a time varying quantity. Here o is called epoch or initial phase. A. If particle at t = 0 is at equilibrium position. (y 0) y= A sin ot B. If particle at t = 0 is at extreme right position (y=A) y= A cos ot o Velocity of particle in SHM. dy Vp = = OA cos (ot ± ¢) dt If at t = 0 particle is at origin. Vp = mA cos wt = wA? y2 Acceleration of particle in SHM ap=-a A sin ot, att=0 particle is at mean position.
