Part 1: Window Method
Exercise 1.1: Spectral analysis
(a) Magnitude spectrum
H( f )
%here we will de
Dynamics of Rigid Bodies
A rigid body is one in which the distances between constituent particles is constant
throughout the motion of the body, i.e. it keeps its shape.
There are two kinds of rigid body motion:
Rectilinear forces acting.
: :3: Datum: TeSt 6' 8
I 1. anlte do mzhnmru uveden rmzy v2 sprmm tunm. Ergnzen Sie im
Gesprch; die angegehenen- Ansdrcke in der Iric-htigen Fnrn1.
"Anna, gehen wir morgen in die Stadt? Elder du schon lms ?"
- Na gut, WiI knnen die Geschifte . Elsa ruf
Dynamics (Newtons Laws of Motion)
1) Given all the forces acting on a body, predict the subsequent (changes in)
2) Given the (changes in) motion of a body, infer what forces act upon it.
Review of Newtons Laws:
The study of the motion of a body along a general curve.
the unit vector at the body, tangential to the curve
the unit vector normal to the curve
Clearly, these unit vectors change with time, uT (t ), u N (t
Exercise Class Week 1 Vectors - Answers
1. Write down the length r and the angle measured anticlockwise from the x-axis of
each of the vectors a to e in the diagram. Not much to explain here note that angles are
measured anticlockwise, because this is ang
Part 1: Block processing method
Exercise 1.1: Filtering a random signal by direct convolution
% Laboratory 2
% Exercise 1.1
x = 5*rand(1,50)-2; %
here we create 50 random
numbers in range (-2,3)
h = [1/8 1/4 1/4 1/4
1/8]; % entering filter
Part 2: Signal generation, sampling and quantization
Exercise 2.1: Basic digital signals
N = 10;
% number of
n = -N/2:N/2;
d = [zeros(1,N/2) 1
Part 1: Spatial Domain Methods
Exercise 1.1: Pixel operations
(a) Luminance conversion
the original image in RGB
subplot(121) % fistly we show
the input image which is
subjected to luminance
Part 1: Filter responses and pole/zero pattern
Exercise 1.1: I/O equation
(a) Transfer function
H (z )
y ( n )=1.5 y ( n1 ) 0.9 y ( n2 ) + x ( n )+ 0.7 x ( n1 )+ 0.6 x ( n2 )
Y ( Z )=
1.5 Y ( z) 0.9 Y ( z)
0.7 X ( z) 0.6 X (z)
+ X ( z )+
Exercise Class Week 4 Circular Motion
1. A space station consists of a cylindrical shell of inner diameter 20m. It rotates around
its axis to give artificial gravity of 1g at the floor (the inner surface of the shell).
a: Calculate the speed v of the floo
Exercise Class Week 3 Dynamics
1. State Newtons First Law of Motion. A body remains at rest or in a state of uniform
motion unless acted upon by an external force.
What principle does it express? The Principle of Relativity
2. State Newtons Second Law of
Find the general (ALL) solution to the equation 2sin(2 x) + 1 = 0 :
In terms of radians and degrees.
2sin(2 x) + 1 = 0
sin(2 x) =
The first solution, x1 (principle solution) related to sin = is (
Oscillations and Waves
For oscillations of a mass m suspended from a massless spring of strength k, the displacement from
equilibrium can be expressed as
x(t) = Asin(0 t + ),
where A and are unkwnown constants and the angular frequency 0 is d
Exercise Class Week 2 Statics and Kinetics
1. A block is resting on an inclined ramp which is at the angle of 30 to the horizontal.
Friction is keeping the block stationary. The block weighs 1kg.
a: Sketch the ramp and block.
b: On your sketch, d
Exercise Class Week 5 Rigid Bodies
1. A bicycle wheel weighs 1kg, all of which is at the rim (i.e. neglect the hub). Its
diameter 2r is 0.7m. If it rotates at = 10 rads1,
a: Calculate the speed of the rim, v: r = 3.5ms1
b: Calculate the momentum, p: mv =