- #1

Connorm1

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## 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

w

_{d}=w

_{o}√(1-ζ^2)

Time to peak overshoot = π/w

_{d}

overshoot = e

^{-(ζπ)/(√(1-ζ^2))}

## The Attempt at a Solution

So with this in mind for

a)

w

_{d}=(1*10

^{3})√(1-0.5^2) = 866.025

Time to peak overshoot = π/w

_{d}= 0.00363seconds

overshoot = e

^{-(ζπ)/(√(1-ζ^2))}= 0.16303

b)

w

_{d}=(2*10

^{3})√(1-0.2^2) = 866.025

Time to peak overshoot = π/w

_{d}= 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