BMED254002
Spring 2014
Homework #4
Question 1)
Rank the following three structures in order of highest stress to
lowest stress.
A. A Cylinder with a diameter of 3mm a height of 1mm and a
load of 100N applied perpendicular to the circular face
B. A Cylin
BMED254002 Biomechanics
Spring 2014
Homework #2
Question 1)
a) Determine the x,y, and z scalar components of the force.
b) Express the force in Cartesion vector form
Question 2)
Find all forces at A, B, and C.
Question 3)
Determine the forces in cables
BMED254002 Biomechanics
Spring 2014
Homework #3
Question 1)
The pipe shown is
fastened to wall.
Assume A acts as a
fixed or built in
support.
a) Draw the Free
Body Diagram
b) Determine the
reactions at this
support when the force
shown is applied at B.
BMED254002
Spring 2014
Homework #5
Question 1)
The grain of a wooden member forms an angle of 15o with the
vertical. For the state of stress shown, determine:
a) The inplane shearing stress parallel to the grain
b) The normal stress perpendicular to th
Andrew Dumont
Homework 6
Due: 4/19/2016
1. A) The image SNR is directly proportional to the square root of the total number of detected
gamma rays. So, doubling the injection dose should double the gamma rays, therefor increasing
the SNR to 1.4 times the
Homework #1, due: 2/11
Andrew Dumont
661164936
1. A system in general is anything that accepts an input and produces and output in
response. This output is determined by the input, system properties and a set of initial
conditions. What makes a system lin
Andrew Dumont
Homework #3
1. Work By Hand:
The index of results is in the bottom left of the work and it is as follows:
(x * y)[n] = 1, n = 1
= 3, n = 2, 4
= 5, n = 3
= 0, others
2. MATLAB Code:
y = [1 1 1 1 1]
y1 = conv(y,y)
y2 = conv(y1,y)
y3 = conv(y2,
Andrew Dumont
Bioimaging HW 2
1.
a. The Bridge is not balanced
b. R3 = R4
R2
R1
R2
R1
= 1.5 and R3 = 480, so 480/1.5 = 320
R4 = 320
c. RB = 320, so R4 = 320 (1.1) = 352
S = VCC
k
2
(1+ x+ k )
Vcc = 100 V, x = 0.1, and k =
R 1 R2
=
RB R3
= 0.25
.25
S = (
Andrew Dumont
Homework 8
Due: 5/9/2016
1. The equation for the transmission coefficient is:
T = 1 R and the reflection coefficient is: R =
I r Z 2Z1
=(
)
Ii
Z 2 +Z 1
Z 2Z 1
If you put this in the first equation you find T = 1  ( Z 2 +Z 1 )

2
2
Muscle t
Andrew Dumont
Homework 5
Due: 4/8/2016
1. Xrays are produced by a process called Bremsstrahlung or breaking radiation. In an xray tube there are electrons and a metal block, the electrons are accelerated towards the
metal block. When the electrons hit th
Andrew Dumont
Homework #4
1. a) If a function x(t) contains no frequencies higher than A hertz, it is completely
determined by giving its ordinates at a series of points spaced 1/(2A) seconds apart
b) The causes of aliasing are is the reconstruction of th
Andrew Dumont
HW 4 Matlab
1) Script:
ab = [a,b];
[R,C] = size(ab);
steptri = 0;
for j=1:R1
for i=j+1:R
steptri = steptri+1;
ab(i,j:C) = ab(i,j:C)  ab(i,j)/ab(j,j)*ab(j,j:C);
if ab ~= triu(ab)
disp('Find x Step')
disp(steptri)
disp(ab)
end
end
end
x = ze
Andrew Dumont
Homework 8 Matlab
1)
Code for Problem 2:
Function:
function change = Phase (t,y)
Ca = y(1);
T = y(2);
change = [16.67  .0167*Ca  1.2E9*Ca*exp(8750/T)
16.3  .0516*T + 2.51E8*Ca*esp(8750/T)];
end
Script:
close all
clear all
clc
T_Equal =
Andrew Dumont
Homework 6 Matlab
4)
Script:
clear
clc
h = 0.1;
y = [5 4];
yfunc = @(t) 16.*exp(2*t)  11.*exp(3*t);
for i = 1:19
y(i+2) = (5*h + 2)*y(i+1)  (6*h^2 + 5*h + 1)*y(i)
end
t= 0:.1:2;
[y_anal] = yfunc(t);
plot(t,y)
hold on
plot(t,y_anal)
hold of
Andrew Dumont
Homework 6 Matlab
4)
Script:
clear
clc
h = 0.1;
y = [5 4];
yfunc = @(t) 16.*exp(2*t)  11.*exp(3*t);
for i = 1:19
y(i+2) = (5*h + 2)*y(i+1)  (6*h^2 + 5*h + 1)*y(i)
end
t= 0:.1:2;
[y_anal] = yfunc(t);
plot(t,y)
hold on
plot(t,y_anal)
hold of
Andrew Dumont
Homework 4 Matlab
2)
Script:
clc
clear all
t
h
y
i
=
=
=
=
0;
.1;
5;
1;
for t = .1:h:2
y(i+1) = y(i) + h*(y(i);
i = i + 1;
end
t = [0:h:2];
hold on
plot(t,y)
analytical = 5*exp(t);
plot(t,analytical,'y')
y(i+1) = y(i) + h*(y(i)
Command Wi
Matlab and Toolboxes
Matlab
A highlevel language and interactive environment that
enables you to perform computationally intensive tasks
faster than with traditional programming languages
such as C, C+, and Fortran.
Matlab toolboxes
Optimization toolbo
Homework 10
Problem 1: State Space and Transfer Function Model Development
The process of drug ingestion, distribution, and subsequent metabolism in an individual may be
represented by the simplified diagram shown below.
Bloodstream
Gastrointestinal Tract
Homework #5
Problem 1: Interpolation using Lagrange polynomials
You are given the follow data set from an experiment:
x
f(x)
1
10
4
5
6
2
9
1
Use Lagrange polynomials to interpolate at the points x = 3, x = 5, and x = 7.
Problem 2: Solution of second orde
Homework 8
Problem 1: Phase Plane Analysis in MATLAB
Write your own code for performing phase plane analysis. Hand in the code.
Problem 2: Reactor Model
The model describes a reactor where A is converted to B. The mathematical description of the
model con
Homework #1
Problem 1:
Consider the Michaelis Menten reaction scheme which includes an intermediate:
Derive the rate expression by making the common assumptions for the Michaelis Menten
kinetics.
Problem 2:
You are given the following reaction network (No
Homework #7
Problem 1: Numerical Solution of 1st order ODE
Consider the following ODE:
dy
y with initial condition y(0) = 5.
dt
a) Use a 4th order RungeKutta method to solve the ODE. Use h = 0.1 and compute the first
two steps. Show all your work (inclu
Homework #2
Problem 1: Solution of System of Linear Algebraic Equations
Consider the following system:
v1
A
v2
B
b1
v3
C
b2
Assume that the fluxes entering and leaving the system are known and given by:
b1= 2 and b2= 1
Compute v1, v2, and v3 using the Gau
Homework 9
Problem 1: Initial and Final Value Problem
Consider the following nonlinear ODE:
dy
y3
dt
a) For y(0) = 10, solve the ODE numerically using a forward finite difference approximation
of the derivative. Simulate the system from 0 to 2 using h =