UTAH STATE UNIVERSITY
ELECTRICAL and COMPUTER ENGINEERING DEPARTMENT

ECE 3620 Oct. 26, 2008

Homework: # 6

Due Oct. 3, 2008

For each problem, you must show your work!

1. 2.4-16(a,b,c,d)
2. 2.4-18
3. 2.6-1
4. A system
   
   $$(D^2 + 4D + 3)y(t) = (D+5)f(t)$$
   
   
   with initial conditions $y_0(0) = 2, \ydot_0(0) = 3$ is driven by a function
   
   $$f(t) = e^{-4t}u(t).$$
   
   
   Determine:
   1. The zero-input response
   2. The impulse response
   3. The zero-state-response
   4. The total response. Identify the natural and forced response components of the response.
5. A system
   
   $$(D^2 + 4D + 13)y(t) = 4(D+2)f(t)$$
   
   
   with initial conditions $y_0(0) = 5, \ydot_0(0) = 15.98$ is driven by a function
   
   $$f(t) = e^{-2t}u(t).$$
   
   
   Determine:
   1. The zero-input response
   2. The impulse response
   3. The zero-state-response
   4. The total response. Identify the natural and forced response components of the response.