Step response and peak response of a transfer function

[mattbrrtt]

Homework Statement

The open loop transfer function to a unity negative feedback system is given as:

G(s)=50/s(s+10)

Homework Equations

Unity feedback is used in this problem, and the system input is a step function.

Y(s)=50/s(s^2+10s+50)

The Attempt at a Solution

I have attached my work.

I think the difficulty I am having is determining the damping factor. 10 doesn't work.

Thank you.

 

[viscousflow]

In the document provided it shows you how to solve for dampening and natural frequency:

$$s^2 + 2 \zeta \omega_ns + \omega_n^2$$ and $$s^2 + 10s + 50$$

simply match the coefficients.

 

[mattbrrtt]

I was able to solve this problem with the aid of Matlab, but 10 can not be used as a damping constant, or the system would be overdamped, and not have the response that was needed. I was able to conclude the damping constant with the use of the software I have, but would like to be able to figure it out. I have corrected everything else in the attachment except the damping constant.

Thank you.