Unit step response of a first-order system with transfer function  is

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  1. 1 – e-t/τ
  2. 1 + e-t/τ
  3. 1 + et/τ
  4. 1 – et/τ

Answer (Detailed Solution Below)

Option 1 : 1 – e-t/τ
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ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins

Detailed Solution

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Concept:

Y(s) = X(s) . G(s)

X(s): Applied input.

G(s): transfer function

Y(s): Output response

A unit step input is defined as u(t). Its Laplace transform is given by:

Calculation:

The transfer function is given as:

The unit step response is the response when the input is a unit step function, i.e.

Using Partial fraction, we get:

On solving it, we’ll get:

Taking the Inverse Laplace Transform, we get:

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