Download Do the following for the system

Example
A rotational mechanical system is shown schematically as
follows. Given that:
J  2 kg  m2 , D  4 N - m  s/rad , and K  8 N  m/rad
T ,
K
J
D
Do the following for the system
1.
Find the differential equation. (2  4  8  T )
2.
Find the transfer function G(s) = θ(s)/T(s). ( G(s) 
3.
Find the poles.( s  1
4.
Find ζ and ωn.( 
5.
Evaluate %OS, Ts, Tp, and Tr of the step response.
3j
1
2S  4s  8
2
)
)
 0.5,   2 rad/s)
( %OS  16.3, Ts  4 sec, Tp  1.8 sec, Tr  0.82 sec )
6.
Find the analytical expressions for the frequency response.
( G( jw) 
1
(8  2 )  16
2 2
2
, G ( jw)   tan 1
4
8  2 2
)
7.
Sketch the Bode plots of the system.
8.
Determine the system ouptut, θ(t), in the steady state if the system input
5

is T (t )  5 sin( 2t ). (  (t )  8 sin( 2t  2 ) )
9.
Suppose this system is the plant of a unity feedback system, detemin the
system type (type 0) find the steady-state error of the feedback system if
the input is a step. (8/9)