E E 238 B1 - Winter 2012 HW #10

Homework Assignment # 10Due: Tuesday, April 10, 2012 16:00pm

testInstructions:

1. Please ensure that your name and ID number are clearly written on your assignment.

2. Please submit your assignment before 16:00 pm on the due date. The assignment box is located in the

ETLC Atrium (second floor), and is marked by E E 238 B1.

Assignment Problems:

1. (10 points)(Lathi 6.3-2 (c)) Solve the following differential equation using the Laplace transform.

Determine the zero-input and zero-state components of the solution.

(D2 + 6D + 25)y(t) = (D + 2)f(t) if y(0−) = y(0−) = 1 and f(t) = 25u(t).

2. (10 points)(Lathi 6.3-5 (b)) For the system described by the following differential equation, find

the system transfer function:

d3y(t)

dt3+ 6

d2y(t)

dt2− 11

dy(t)

dt+ 6y(t) = 3

d2f(t)

dt2+ 7

df(t)

dt+ 5f(t).

3. (10 points)For a system with transfer function

H(s) =s + 5

s2 + 5s + 6

(a) Find the (zero-state) response if the input ise−3tu(t).

(b) For the system, write the differential equation relating the outputy(t) to the inputf(t).

4. (10 points)Find the transfer function from inputF (s) to outputY (s) in the following block diagram:

P(s)

C(s) Q(s)

+F(s) Y(s)

−

+

−G(s)

Figure 1: Block diagram for Problem 4.

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