Q.Compare the electromagnetic oscillations of LC circuit with the mechanical oscillations of block-spring system qualitatively to find the expression for angular frequency of LC oscillator.

Setting up the analogy. The electromagnetic oscillations of an LC circuit can be compared directly, term by term, with the mechanical oscillations of a spring-mass system already met in Class 11. Both systems oscillate between exactly two forms of energy: the LC circuit between the capacitor's electrical energy and the inductor's magnetic energy; the spring-mass system between the spring's potential energy and the mass's kinetic energy.

The quantity dictionary. Matching corresponding elements and their energy formulas pairs charge q with displacement x; current $i=dq/dt$ with velocity $v=dx/dt$; inductance L with mass m (both measuring inertia -- resistance to a change in current, or in velocity); and the reciprocal of capacitance $1/C$ with the spring's force constant k. The electrical energy $\tfrac12(1/C)q^2$ then matches the spring's potential energy $\tfrac12kx^2$ term by term, and the magnetic energy $\tfrac12Li^2$ matches the kinetic energy $\tfrac12mv^2$ term by term, so total energy $U=\tfrac12(1/C)q^2+\tfrac12Li^2$ corresponds exactly to total mechanical energy $E=\tfrac12kx^2+\tfrac12mv^2$. …