Theoretically frequency and time domain analysis are almost equivalent in most of the cases (Laplace transform should exist. There are effects of Gibbs phenomenon so they are not exactly the same).

But practically you cannot completely determine the frequency system up to 100% accuracy (Sinusoidal wave forms are everlasting mathematical entities.) Therefore you will loose some information. Practically both transient analysis and frequency analysis will loose some information so one will work better than the other in some cases. That is why frequency analysis is used for steady states and time domain analysis for transient case.

The same is true for time series analysis. Previous frequency domain analysis methods were superseded by time domain analysis methods to predict economic behavior in early 20th century.

Hello Mr Shalabh Kumar Mishra

In one phrase I can answer both of your questions but that wouldn't be very convenient, so I am trying to explain a little bit.

First of all, you asked What is the utility of transient analysis?

The answer is it's a type of mathematical simulation to understand the circuit's response over time, as well as a method to identify the transfer function of an unknown system. Because the 'Transfer Function' = Laplace Transformation of the 'Impulse Response' of an LTI (Linear Time-Invariant) system having initial condition zero. Hence, in this way, we can make a conceptual mathematical model of an unknown system, mostly filters and actuators.

Your next question is about "Frequency analysis".

Well, it's obviously a necessary step to analyze a filter but not sufficient for a real-life system. Because for the real-life system we can expect many external features which we always can't mathematically simulate. As example I can mention the tolerance of passive components, the junction capacitance of active components, the effect of ambience and many more.

It's necessary as it gives us almost 90% - 95% idea about the cutoff frequency, the phase difference and the time response. Which are actually the obligatory attributes to design any system.

These are the answers to your question, I hope they can satisfy you. If you need more detail, I will be glad to help you. Good Luck!!

I can give an example of a filter that has a certain frequency response but exciting some components (Capacitor/inductor) with certain initial conditions can lead to transient responses that can damage some components.

I think transient analysis is about the system's reaction just after having the input by knowing the rise time, overshoots, delay time and most importantly settling time. Whereas, the frequency domain analysis shows the overall behavior, especially after achieving its steady state.