May 16th 20144

Prof. Dr. Maki K. Habib

The American University in Cairo School of Sciences and Engineering Mechanical Engineering Department

Dynamic Systems MENG 375/3705 (Spring 2014)

Assignment 7 BONUS

(Problems should be worked by the exam day May 21st)

1. Given the system in Figure below, find the transfer function. Then, find the damping D to yield a 20% overshoot in the output angular displacement for a unit step input in torques. Finally, find the rising time and the peak time of this system after deciding the suitable damping D.

2. For the circuit shown in the Figure below.

Find the Transfer function of this Circuit Vc(s)/Vi(s). Then, find the values of R2 and C to yield damping ratio of 0.6 and settling time of 0.02 sec for a voltage across the capacitor, with vi (t) as a unit step input. Finally, find the rising time and the peak time of this system after deciding C.

May 16th 20144

Prof. Dr. Maki K. Habib

3. Figure (a) below shows a mechanical vibratory system. When a 3 lb of force (step input) is applied to the system, the mass oscillates as shown in the response curve in Figure (b). Determine the values of m, b and k of the system from the data given in the response curve.

4. Determine the values of K and Kh such that the close-loop system shown in Figure a has the pole plot shown in Figure b Then, find the steady state error for a ramp input 3tu(t). Finally, find the rising time, peak time and settling time of this system, and the response c(t) for a unit step input. Assume J = 3 kg-m2, and b = 2 N-s/m.

Figure a Figure b

5. Find M and K shown in the system of the Figure below to yield x(t) with 30%

overshoot and 5 second settling time for a step input in motor torque Tm(t). Then, fine the rising time and the peak time after deciding M and K.

May 16th 20144

Prof. Dr. Maki K. Habib