II. A digital control system has the following difference equation: y[n] = 2.0 x[n] - x[n-1] + 1.2 y[n-1] - 0.48 y[n-2]

a. Find the transfer function H(z) for this system.

b. Draw the digital circuit for H(z). A digital circuit includes sum, multiplication, and delay components.

c. Use MATLAB to draw the pole-zero diagram for the above system.

d. Use MATLAB to derive and plot the impulse response of the system.

e. With the help of MATLAB find and explain the response of the system to the input x[n]=(1-0.5e-n )u[n], where u[n] is a step function. What is the steady-state solution, i. e. when n becomes very large?

Note: please answer be precise

At 12 noon, the count in a bacteria culture was 400; at 4: 00 pm the count was 1200 let p(t) denote the bacteria cou population growth law. find: (a) an expression for the bacteria count at any time t (b) the bacteria count at 10 am. (c) the time required for the bacteria count to reach 1800.

Aturning operation is performed with following conditions: rake angle of 12°, a feed of 0.35 mm/rev, and a depth of cut of 1.1 mm. the work piece is aluminum alloy 6061 with t6 heat treatment (a16061-t6). the resultant chip thickness was measured to be 1.0 mm. estimate the cutting force, fc. use shear stress of 207 mpa and coefficient of friction on the tool face of 0.6.

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj