Example A rotational mechanical system is shown schematically asfollows. Given that:

Do the following for the system

1. Find the differential equation. ( )

2. Find the transfer function G(s) = θ(s)/T(s). ( )

3. Find the poles.( )

4. Is this system stable or not? Why? (Stable as all poles are in the LHP)

5. Find ζ and ωn.( )

6. Evaluate %OS, Ts, Tp, and Tr of the step response.

( )

7. Find the analytical expressions for the frequency response.

( )

7. Determine the system ouptut, θ(t), in the steady state if the system input is . ( )

8. Suppose this system is the plant of a unity feedback system, find the steady-state error of the feedback system if the input is a step. (8/9)

,T

D

K

J

m/radN 8 and ,s/radm-N 4 ,mkg 2 2 KDJ

)2sin(5)( ttT

T 842

842

1)(

2

sSsG

js 31

rad/s 2 ,5.0

sec82.0 sec,8.1 sec,4 ,3.16% rps TTTOS

21

222 28

4tan)( ,

16)28(

1)(

jwGjwG

)2

2sin(8

5)(

tt