T WO DIFFERENT PHENOMENA , SAME MATHEMATICAL TREATMENT

T WO DIFFERENT PHENOMENA , SAME MATHEMATICAL TREATMENT You may like to compare the treatment of a forced damped oscillator discussed in Section . of Class XI physics textbook, with that of an LCR circuit when an ac voltage is applied in it. We have already remarked that Eq. [ . (b)] of Class XI Textbook is exactly similar to Eq. ( . ) here, although they use different symbols and parameters. Let us therefore list the equivalence between different quantities in the two situations: Forced oscillations Driven LCR circuit cos d x dx b kx F dt dt sin L v Displacement, x Charge on capacitor, q Time, t Time, t Mass, m Self inductance, L Damping constant, b Resistance, R Spring constant, k Inverse capacitance, / C Driving frequency, ω d Driving frequency, ω Natural frequency of oscillations, ω Natural frequency of LCR circuit, ω Amplitude of forced oscillations, A Maximum charge stored, q m Amplitude of driving force, F Amplitude of applied voltage, v m You must note that since x corresponds to q , the amplitude A (maximum displacement) will correspond to the maximum charge stored, q m . Equation [ . (a)] of Class XI gives the amplitude of oscillations in terms of other parameters, which we reproduce here for convenience: