Contro Systems - Using Partial Fraction Expansion on Transfer Function

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Homework Statement


A system has damping ratio 0.5, natural freq. 100 rad/s, DC gain of 1. Find the response of the system to a unit step input.


Homework Equations



Im having trouble doing the partial fraction expansion.

The Attempt at a Solution



I have attached a word document using the equation editor.
 

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on Phys.org
cover up rules? equating coefficients?