(1)

For the given transfer function

1. Derive y( t) with respect to a unit-step input and an impulse input.

2. What are the values of y( t) at t = 0 and t = ? with respect to a unit-step input?

(2)

For the given ODE,

y" + y' + y = sin ?t,

with initial condition y(0) = y'(0) = 0. What are the characteristic features of y( t)? What is y( t) when t ? ??

(3)

For the given ODE,

sketch the probable time-domain response if f( t) is a unit-step function.

(4)

Derive time-domain function y( t) of the following Laplace transforms

1. Y( s) =

2. Y( s) =

3. Y( s) =

4. Y( s) =

(5)

Find the partial fractions of the following transfer function:

(6)

For the following transfer function,

and given that the input x( t) is a unit-step function, what is y( t) as t ? ?? Under what condition, as related to the property of the transfer function, is this result valid?

(7)

For the following transfer function and a unit-step input, sketch qualitatively the time response y( t):

Explain how each "term" in the transfer function may contribution to your sketch.

(8)