Modern University for Modern Sciences and Arts

Faculty of Engineering Automatic Control System

ESE 346/ESE416

Sheet 1 ----------------------------------------------------------------------

Problem 1: For the RC Circuit shown in Fig. 1.

a- Find the differential equation that relates the output voltage and the input voltage

b- Find the differential equation that relates the current and the input voltage

Fig. 1 Problem 2

For the RL Circuit shown in Fig. 2. a- Find the differential equation that relates the output voltage and the

input voltage b- Find the differential equation that relates the current and the input

voltage

Fig. 2

Vi Vo

C=1 F

R=10 K

Vi Vo

L=1 mH

R=10 K

Problem 3 For the RLC Circuit shown in Fig. 3.

a- Find the differential equation that relates the output voltage and the input voltage.

b- Find the differential equation that relates the current and the input voltage.

c- Determine the unit step response.

Fig.3 Problem 4:

Obtain the mechanical model of the system shown in Fig.4

Fig. 4

Vi Vo

C=1 F

R=10 K

L=1 mH

M

F

K B

x

Problem 5: Consider the mechanical system. Write the differential equation of the system shown in Fig.5

Fig. 5

Problem 6:

Consider the mechanical system. Write the differential equation of the system shown in Fig. 6

Fig. 6

M2 x

K

M1

B1

B2

F(t)

M x

K1 B1

F(t)

K2 B2