Q1(20 points). A complex function is defined as:
Find f(t) with inverse Laplace transform method.
Q2

Q1(20 points). A complex function is defined as:

Find f(t) with inverse Laplace transform method.

Q2 (30points). A system is defined by the following differential
equation:

Assume all initial conditions are zero.

Find the transfer function. WhatA????1s order the system is?

Find the zeros (infinity zeros are also needed to be include if
exist), poles of the transfer. If the order of a zero/pole is
higher than 1, point it out its order.

Get the impulse output of the system.

Get the output of the system if the input is a unit-step signal.
The inverse Laplace transform method is required.

Q3(30 points). Consider the system described by:

Obtain the transfer function of the system.

Obtain the differential equation of the system.

Draw the block diagram with the state-space representation of
the system.

Q4(20 points): Simplify the block diagram and get the transfer
function .