SIMPLE HARMONIC MOTION
ISC SYLLABUS
Oscillations: Periodic motion, time period, frequency, displacement as a function of time, periodic functions. Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring, restoring force and force constant; energy in S.H.M., Kinetic and potential energies; simple pendulum and
derivation of expression for its time period.
Elaboration of Syllabus:
Simple harmonic motion. Periodic motion, time period T and frequency f,
f=1/T; uniform circular motion and its projection on a diameter defines SHM;
displacement, amplitude, phase and epoch, velocity, acceleration, time
period; characteristics of SHM; Relation between linear simple harmonic motion and uniform circular motion. Differential equation of SHM, d2y/dt2 +ω2 y=0 from the nature of force acting F=-k.y; solution y=A.sin(ωt+φ0) where ω2 = k/m; obtain expressions for velocity, acceleration, time period T and frequency f. Graphical representation of displacement, velocity and acceleration.
Examples, simple pendulum, a mass m attached to a spring of spring constant k. Derivation of time period of simple harmonic motion of a simple pendulum, mass on a spring (horizontal and vertical oscillations) Kinetic and potential energy at a point in simple harmonic motion. Total energy E = U+K (potential +kinetic) is conserved. Draw graphs of U, K and E Verses y.
