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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
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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
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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