Entrance Test for Master Course MSST
at VGU Winter Semester 20011/12
09.07.11, 9.00 – 11.00 pm
Last name:……………….…SOLUTION.…………………………….…….
First name:………………………………………………………………………
Duration: 120 Minutes
Expedients: None
Please note down your solution in the gabs left free on the paper.
Only these solutions will be evaluated!
For your calculations use the back of the pages.
You can use additional paper for your calculations and sketches
which will not be evaluated!
Evaluation: total points 100
Task
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11
T12
T13
T14
T15
T16
T17
T18
T19
T20
total
Points
10
10
5
10
10
10
4
6
2
3
2
3
3
3
3
2
2
2
3
7
100
gained
Professors Signature:____________________________Date:____________
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 1/8
1.
Task
Given the following differential equation:
a ⋅ y (t ) + b ⋅ y (t ) = c ⋅ x (t ) .
1.1. Derive a general expression for Y(s) in the Laplace Space.
Y ( s) =
1
b
s+
a
⋅ y ( −0) +
c
a ⋅ X ( s)
b
s+
a
1.2. Calculate the solution for y(t) with the initial condition
y(0) = 1, a = 1, b = 2, c = 4 and x ( t ) = σ (t ) (step function).
Y (s) =
2.
1
4
L−1
⋅ (1 + ) 
→ y(t) = 2 − e−2t
s+2
s
Task
Given the following Boolean expression:
y = a ∧b∧c∨b∧c∨a ∧b∧c
2.1. Simplify the function.
y = abc + bc + abc = (b + ab) ⋅ c
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 2/8
2.2. Fill out the truth table for y:
3.
a
0
b
0
c
0
y
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
Task
Calculate the integral:
1
∫0 (1 + x)2 dx .
1
1
1
1
∫0 (1 + x)2 dx = − 1 + x 0 = 0.5
1
4.
Task
Given is the following electrical circuit:
Fig. 1: Filter Circuit
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 3/8
4.1. Derive the transfer function G(s) of the circuit.
U 2 ( s) =
1 + s 2 LC
⋅ U1 ( s )
1 + s ⋅ L / R + s 2 ⋅ LC
4.2. Which filter characteristic does the circuit show?
Band stopping characteristic
5.
Task
Fig. 2: Operational Amplifier
5.1. Derive the relation between input and output voltage in the complex frequency
domain.
Vout ( jω ) =
−1
⋅ Vin ( jω ), T = R ⋅ C
jωT
Integrator
5.2. Derive the relation between input and output voltage in the time domain.
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 4/8
6.
Task
Vout
Vin
Fig. 3: Transistor Circuit
6.1. Which standard transistor circuit does Fig. 3 show?
Emitter circuit
6.2. What are the resistors R1 and R2 for?
Define the operating point
6.3. What is the effect of resistor R3?
Stabilization by voltage feedback.
6.4. What is the effect of resistor R4?
Stabilization by current feedback.
6.5. Sketch the principle input/output diagram for the resistor circuit in Fig. 3.
6.6. What do you get at the output for a constant input voltage?
No output because of the capacitors.
7.
Task
Make your judgment and tick the respective box.
17161 = 169, 31
6 ⋅ 3,8 ⋅ 15 = 220
= 131
= 342
= 167,82
= 109,0
= 360
= 45, 3
= 187,79
= 225
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 5/8
8.
Task
Continue logically the following number sequence with the next number.
9.
10 5 20 10 30 15 30
3 5 7 9 11 13 15
15
17
1 1 2 6 24 120 720
5040
5 10 12 6 4 8 10 5
3
Task
What is the seven hundred ninety sixth number of the sequence?
0 3 6 9 12 15 .... ?
10.
2385
Task
A roll of 60 m of wall paper should be cut in two pieces so that one is 2/3 of the
other. How long is the shortest one?
24 m
11.
Task
15 boxes with banana are weighing 250 kg. Every box weighs 3 kg.
How many kg’s do the banana weigh?
205 kg
12.
Task
7 workers can do a job within 6 hours. How many workers do we need if would
like to finish the job in 30 minutes?
84
13.
Task
Give are the following patterns:
Fig. 4: Pattern
With witch pattern can you continue the sequence logically? Tick the box of your
choice!
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 6/8
14.
Task
Give are the following patterns:
Fig. 5: Pattern
With which pattern can you continue the sequence logically?
none
15.
Task
Fig. 6: Wheels
In which direction turns the wheel 2? Tick the button of your choice.
A
16.
B
A+B
Task
Fig. 7: Circuit
Is the circuit open or closed? Tick the button of your choice.
Yes, open.
No, closed.
Cannot be decided
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 7/8
17.
Task
Which wheel turns slowest? Tick the button of your choice.
Fig. 8: V-Belt Drive
18.
Task
Fig. 9: Moving Box
In which direction moves the box? Tick the button of your choice.
19.
Task
Level drops.
Level remains the same.
Level rises.
Fig. 10: Glass with water
You hold the glass ball in your hand. Does the water level rise or drop? Tick the
button of your choice.
20.
Task
Implement in a programming language of your choice the following problem: A
function should exchange the values of two variables A and B.
C++:
void swap(float *A, float *B)
{
float temp=*A;
*A=*B;
*B=temp;
}
www.vgu.edu.vn
MSST Mechatronics and Sensor System Technology
Prof. Dr.-Ing. Hans-Werner Dorschner
Entrance Test
09.07.2011
Page 8/8