system dynamics

Part 1) Select one of the systems given below

i)A translational mechanical second order system

ii)A Rotational mechanical second order system

iii)An Electrical second order system

1. Write the differential equation and assign numerical values for the components yourself,
2. Obtain the corresponding transfer function for your system,
3. Write the characteristic equation. Find the damping ratio and natural frequency of your system, explain whether it is Underdamped, Critically damped and Overdamped. Show the location of poles in s-plane. (Fig.1)
4. Obtain the unit step response and plot the response using Matlab by writing an m-file. (Fig.2)
5. Obtain the state-space model by assigning x1,x2, etc. yourself. Plot the unit step response of statae-space model. (Fig.3) Compare with the step response of the transfer function. Are they the same?

Part 2) Assume a second order system with characteristic equation s2+2ns+n2=0

1. Assign a numerical value for n and plot the unit step response of the system in the same figure (Fig.4) for at least 5 different z value so that the system will be Underdamped, Critically damped and Overdamped (for example, between 0
2. Assign z=0.7 and plot the unit step response for at least 5 different value of n on the same figure (Fig.6). Show the location of poles on the s-plane (Fig.7). How do they change as n changes?

IMPORTANT NOTES:

1)Either use different colours or different line types (dotted line, solid line, etc.) in the same figure. Give a number to the figure, add titles and captions as shown below.

2)Explain each equation, figure and write your comments on the results.

3)Add your m file code at the end of each part.

Unitstep response for GS Ampude - 25 05 -15 IS Time (soci Figure 1. Unit step response for different value for wn=1 rd/sec