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The LC oscillation is similar to the mechanical oscillation of a blockattached to a spring. The lower part of each figure in Fig. 7.19 depictsthe corresponding stage of a mechanical system (a block attached to aspring). As noted earlier, for a block of a mass m oscillating with frequencyω 0, the equation isd xdtwww.GOALias.blogspot.com22ω2 0+ x = 0Here, ω0= k/m , and k is the spring constant. So, x corresponds to q.In case of a mechanical system F = ma = m (dv/dt) = m (d 2 x/dt 2 ). For anelectrical system, ε = –L (di/dt ) = –L (d 2 q/dt 2 ). Comparing these twoequations, we see that L is analogous to mass m: L is a measure ofresistance to change in current. In case of LC circuit, ω0= 1/ LC andfor mass on a spring, ω0= k/m . So, 1/C is analogous to k. The constantk (=F/x) tells us the (external) force required to produce a unitdisplacement whereas 1/C (=V/q ) tells us the potential difference requiredto store a unit charge. Table 7.1 gives the analogy between mechanicaland electrical quantities.Alternating CurrentTABLE 7.1 ANALOGIES BETWEEN MECHANICAL ANDELECTRICAL QUANTITIESMechanical systemMass mForce constant kDisplacement xVelocity v = dx/dtMechanical energySlectrical systemInductance LReciprocal capacitance1/CCharge qCurrent i = dq/dtElectromagnetic energy1 1E = kx + mv2 22 2U21 q 1= + Li2 C 22Note that the above discussion of LC oscillations is not realistic for tworeasons:(i) Every inductor has some resistance. The effect of this resistance is tointroduce a damping effect on the charge and current in the circuitand the oscillations finally die away.(ii) Even if the resistance were zero, the total energy of the system wouldnot remain constant. It is radiated away from the system in the formof electromagnetic waves (discussed in the next chapter). In fact, radioand TV transmitters depend on this radiation.257