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This Book intends to apply Lagrange's and Hamilton's principles in solving Classical problems constrained to oscillate over a very small distance. It introduces to Dynamics of System of particles, Rigid body, Solve inertia tensor for rigid bodies and relates to Rotational kinetic energy and Angular momentum with inertia tensor. It also applies Lagrange equation of motion to solve Amplitude for Small Oscillation and explains the relation between equilibrium and small Oscillation and wave propagation, wave equation, reflection, diffraction and interference. The approximations followed are very essential in studying physical systems perturbed from their equilibrium position by comparatively very small potential.