Ramos 1
Modeling and Analysis
Adela Ramos
Simulink #1
1. (1) A clothes iron has a sole plate weighing 1.75 kg with an exposed area of 0.05 m2. The
sole plate is made of steel, which has a heat capacity of 450 J/kgoC, and the heat transfer
coefficient for
TEST 2 Problem 2 Fall 2014
2
d 2T
dT
8
16 T 0
2
dt
dt
with T (0) 20 oC and
dT
dt
0
0 C
t 0
min
.
Taking the Laplace transform of the differential equation, and solving for the Laplace of the
dependent variable,
2 s 2T ( s ) 2 s (20) 2(0) 8sT ( s ) 8(20)
TEST 1 Fall, 2015
Problem 1 (20 points)
Find the complete solution to
2
d12w+2d—T+5T=t with T(0)=0and—6£1z =2
dt d t d t [:0
Problem 2 (20 points)
Suppose that the following equation describes the concentration of a component in a
fermentation reaction.
Ruth Fabian
Mini Project II
Modeling Analysis
November 2, 2015
Given:
W1= 200 kg/min
W2= 100 kg/min
h=3.24 m
146
dh
+166.7 h=w1 ( t ) + w2 (t)
dt
(1)
146
dhl
+ 46.34 hl +w 1 ( t ) +w 2 ( t )150.14
dt
(2)
The program below for the differential equation is
Chapter 3
Problem 31
a)
3
Using initial condition,
Thus,
0
3 ;
and
1
0
b)
2
0
0
2 ;
and
Using initial condition,
Thus,
1
1
c)
1
Using initial condition,
Thus,
4 1
4 0
0 ;
1 and
4
4
1
4
1
3
4
4
1
d)
0
;
and
1
1
Using ini
Chapter 4
Problem 41
a)
Integrating by parts
1

1
0
1
0
1

1
b)
where a is a constant
1
1
1

c)
cos
1
2
1
1
2
1
2
1
1

2
2
2
1

2
d)
cos
cos
2
1
2
1
1
2
1
2
1

1

1
2
2
2
Prob
Chapter 2
Problem 21
Going Up
+
y
y=0
Assuming no air resistance:
ground
2
1 1
2 2
2
Substituting (2) into (1) and rearranging,
0
3 with
Maximum height is when
35 /
0
From (3)
=>


=> 0
3.57
We can also obtain an expression for
CH
HAPTER 5
Problem 51
m
1 1
or
and
2
,
2 2
3 3
3
3
3
d
e
r
taining the an
lution.
We could reduce the number of equations for ease in obt
nalytical sol
Substitut
ting (3) and (2) into (1) and rearranging,
(
a
0
CHAPTER 9
Problem 91
R 4
+

+
+
L =2H
vS 20 e 4t

t =0

The voltage supply and switch can be mathematically expressed as
20
KVL
0
1 1 . , 2
From R:
2 2 . , 3
3 3
From L:
. , 3
.
.
.
,
.
Substituting (2), (3) into (1):
0
With
0
0
PROBLEM SET MODULE 1
Problem 1
Problem 1.1a
Problem 2
Problem 1.1b
Problem 3
Consider the tank of Section 11 and its steady state condition of w1 200 kg min ,
w2 100 kg min and h 3.24 m . Suppose that at time equal to 10 min w1 changes to
400 kg min and
Adela Ramos
04/17/2014
Simulink #3
1. (a) Show that the voltage drop across the load resistance R is given by:
Submit your block diagram and scope.
(b) Show that the voltage drop across the load resistance for this circuit is given by
the equation:
Submit
Chapter 4
Problem 1
Using the definition of the Laplace transform, derive the transforms F(s) of the following
functions
a) f (t ) t
b) f (t ) e a t where a is a constant.
c) f (t ) cos t where is a constant.
d) f (t ) e a t cos t where a and are constant