A system is governed by the different equation based on your student number (abcdefg), such as follows: + + = + , where = 8 ( + + + + + ), = ( + + + + + ) (10 + ) ( + + 4), and = + 2.

For example, if abcdefg is 1234567, then: + + = + , where = 8 (2 + 3 + 4 + 5 + 6 + 7) = 216, = (2 + 3 + 4 + 5 + 6 + 7) (10 + 2) (3 + 6 + 4) = 4212, = 2 + 2 = 4. With this differential equation:

a. Determine the transfer function G(s).

b. Determine the poles and zeroes of the system.

c. Determine the output solution y(t) function when unit step input is applied.

d. Determine the output solution y(t) function when unit impulse input is applied.

e. Determine the steady state value when unit step input is applied.

f. Sketch the output solution

c. including the steady state value.