# Sketch the waveform to represent the transient response

• Connorm1
In summary, the conversation discussed representing the transient response of circuits with different transfer function parameters on a set of common axes. The equations for calculating the peak overshoot and settling time were also mentioned. The conversation then moved on to discussing how to draw these responses on a graph, specifically for a step input. The expert suggested looking up different graphs for step inputs for second order systems and understanding which waveform corresponds to the given values of ωn and ζ. The importance of initial conditions in solving the ODE was also highlighted.
Connorm1

## Homework Statement

Sketch, on a set of common axes, waveforms to represent the transient
response of circuits having transfer functions with the following parameters:

a) ζ = 0.5, ω = 1×10^3 rad s^-1
b) ζ = 0.2, ω = 2×10^3 rad s^-1
c) ζ = 2, ω = 1×10^3 rad s^-1

## Homework Equations

wd=wo√(1-ζ^2)
Time to peak overshoot = π/wd
overshoot = e-(ζπ)/(√(1-ζ^2))

## The Attempt at a Solution

So with this in mind for
a)
wd=(1*103)√(1-0.5^2) = 866.025
Time to peak overshoot = π/wd = 0.00363seconds
overshoot = e-(ζπ)/(√(1-ζ^2)) = 0.16303

b)
wd=(2*103)√(1-0.2^2) = 866.025
Time to peak overshoot = π/wd = 0.00363seconds
overshoot = e-(ζπ)/(√(1-ζ^2)) = 0.16303

c) will have no overshoot as ζ = 2>1 (which means no oscillation).

How do i actually draw these as graphs now? is there more info i need?

do i also need to use
?

What's the input? Step? Delta? Ramp? ...
Given this you can solve your ODE but there are many places to look up under-damped, critically damped, and over-damped 2nd order systems.

This is what I'm unsure of, if it mentioned one of the above i could work through it via my notes... I've only encountered step change input for second order systems. Thus i understand which ones are under-damped (a/b) and which are over-damped c if this is the case. But how do i draw this? only thing i can see from the graph is y(t)=1 but how do i find x(t) & the time period...

Connorm1 said:
This is what I'm unsure of, if it mentioned one of the above i could work through it via my notes... I've only encountered step change input for second order systems. Thus i understand which ones are under-damped (a/b) and which are over-damped c if this is the case.
Assume step input then.
But how do i draw this? only thing i can see from the graph is y(t)=1
Say what? The output is a constant dc voltage? And what graph? You haven't provided one for us to look at.
You have the information you need to draw the output graphs. I suggest looking up the various possible graphs depending on ζ and ω for a step input. Widely available on the web.

rude man said:
Assume step input then.Say what? The output is a constant dc voltage? And what graph? You haven't provided one for us to look at.
Apologies I think I've gotten myself confused... I think I am looking too deep into it. I'll be back when i have some form of graph! Thanks for your help @rude man

Connorm1 said:
Apologies I think I've gotten myself confused... I think I am looking too deep into it. I'll be back when i have some form of graph! Thanks for your help @rude man
Good idea. Google "second order systems responses". The curves will all be there.

@rude man so after searching through second order system responses I have a graph that looks like this. How does it look?

#### Attachments

• TMA 3 Q4 Waveform Sketch.pdf
351.3 KB · Views: 382
That's the idea.
Make sure yu understand which waveform corresponds to your values of ωn and ζ.

You should also understand how your ODE in your post 1 solves to those waveforms. That equation requires one or two initial conditions otherwise you get nothing from it.

## 1. What is a transient response?

A transient response is the behavior of a system or circuit in response to a sudden change or disturbance in its input. It is a temporary response that occurs before the system reaches its steady-state.

## 2. How is a transient response represented?

A transient response is often represented graphically by plotting the output of the system over time. This results in a waveform that shows how the system responds to the input change.

## 3. What factors can affect the transient response?

The transient response of a system can be affected by various factors such as the type of input signal, the characteristics of the system, and the components used in the circuit.

## 4. What does the shape of a transient response waveform indicate?

The shape of a transient response waveform can indicate the stability and performance of a system. A well-damped waveform with minimal oscillations indicates that the system is stable and responds quickly to input changes.

## 5. How can the transient response be improved?

The transient response of a system can be improved by using components with lower resistance and capacitance values, increasing the system's bandwidth, and using feedback and control mechanisms to reduce the effects of disturbances.

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