I shall try to answer the question in a simplistic manner if you please.

1. There are two parts to the current through a RLC circuit ( I am assuming it is a simple series circuit for simplifying the explanation) energised by an AC supply, of which the frequency has been changed suddenly. This is because the earlier current ( before the change of frequency) has charged both the inductor and the capacitor with an internal energy. This energy has to be dissipated and the circuit must also admit the new current with renewed impedance responding to the AC supply at a new frequency.

2. Since the circuit, as you rightly mention is linear, the superposition of both currents is possible.

3. Now the first part of the output current, as you call it, will have the repercussions of the stored energy being dissipated.and will have a magnitude dependent on the original maximum value ( depending on applied voltage and earlier impedance of the circuit at the earlier frequency), the cut-in angle, or point of time when the frequency got changed and its nature- ( over-damped or under-damped or critically damped ) will depend on the relative values of R, L and C. The oscillatory frequency will again depend on the constituent RLC.

4. The second part is due to the circuit responding as a forced response to the applied voltage at a new frequency.

5. If only the transient portion is evaluated, then we do have non-linearity in evidence, but then a non-linear operation, i.e. a sudden change in applied voltage has occurred. Perhaps application of superposition principle is questionable. Yet, in fault analysis, we use a similar analysis. It may be justified as a linearization about the operating point case or because we also have a multi-input system here, and transfer function approach not having applicability.

6. Thankfully steady state analysis is linearity based. 

Let us hope to get more inputs on your interesting question.

After applying Laplace transform to RLC circuit the resulting equations end up with a quadratic equation(with s as the variable) which is non linear. Then how for linear circuit the equation turns out to be non linear. 

Note: s=j*omega, omega=2*pi*f. 

This is what i meant to ask. Give your answer on this edited version of question. 

A second order equation does not mean non-linearity. It is the input to output relationship which indicates non-linearity or otherwise. Quadratic LT just means that the expression for current is critically damped, over-damped or oscillatory.And s= sigma +/_ j*omega

And the most important contradiction that I must point out is that you cannot use LT if there is non-linearity 

The s2 that you point , on the one hand, means that is a second order diferential equation. Maybe you must read a Control Theory book in order to obtain more information about LT and systems. At this point, Professor Balagopalan's answer is better than mine.

In the other hand, the  s2  element in the Transfer Function you obtain means, correct me if I'm wrong, frequency's dependence of the RLC circuit  is about 40dB / decade.

This sounds suspiciously like a homework problem. Think of it this way: An RLC circuit is often used as a band pass filter, right? As such, when AC at various frequencies is applied to it, you should expect the response to vary, and more than that, you should expect the response for most of the frequencies to be equal for two different frequency values. And the response to be lowest or highest, depending how it's designed, at one frequency

So, a quadratic equation will do that.

Just use the formula for impedance for R, L, and C.

Dear Sudha Madam

Thank you for responding my questions posted. I am understanding what you mean to explain but let me re-frame my question in this way:

When the expression for load current in Laplace Domain with V as the input is written it turns out to be quadratic. I do understand that this s2 term indicates second order differential equation in time domain. But my question is not this.

Now if you consider my dependent variable as I(s) and independent variable as omega then the relationship between them is nonlinear. How come is it true for linear circuit?

Or it is like linearity and non-linearity has to be analysed in time domain only. Please Elaborate on this. 

Linearity vs. non-linearity are terms with respect to the time domain.

And - by the way - linearity means a continuously differentiable function (causality not mandatory though present in most cases) - not some kind of staight line !

Perhaps linearity or otherwise has more relevance and is easier to visualize in the time domain, This is true, especially when you linearize about the point of operation, for analysis, where generally you choose a point of time. Else, it is my firm belief that linearity or the lack of it has no time domain restriction.

Coming to Mr. Rajanarayan.s question, may I add that assuming a sinusoidal input with a changing frequency, the LT of the sinusoid is also a quadratic in s.Hence the relation of I(s) in relation to omega is at the most incrementally linear.

For any input other than a dc input, LT has higher orders in s. 

For the particular purpose of you to visualize the concept of linearity, I suggest that you observe that when voltage applied (input) increases, the output current also increases, in proportion or linearly as it also happens when the input trend changes. 

This is enabled only by linear elements, R-L-C

Have I made my point clearer?

Sudha

Thank you all for your participation.