HW 3 Solutions
EA3 Spring 2015
Table of common point deductions
Error
Wrong sign (in equation)
Wrong sign convention (arrow pointing in wrong direction
in FBD, etc)
Missing/wrong unit (when units prov
% EA3 HW4 Problem 5-2: w/o the 100kg mass
% Given values
k = 2000;
b = 1200;
X_spring(1) = -0.02;
% Time interval of dt = 0.01
dt = 0:0.01:8;
% Force values: change between F = 0 and the actual values
5
Exponential Solutions
Last time we learned that Euler integration allows one to approximately solve a ordinary differential equation. What do we do if we have an ordinary differential equation that
3
Newtons Laws
Last time we learned how constitutive laws relate forces to variables describing components, but
what principles do we use to combine those constitutive laws into models of mechanical s
What Does The Word Linear Mean?
The word linear in linear, constant coefcient, rst-order ODEs can cause a lot of confusion.
In many respects, that is because the word linear has two primary uses. One
9
Imaginary Numbers and Eulers Formula
Last time we learned that Newtons laws give us linear, constant-coefcient, rst-order ODEs
for systems with masses. We know that 1) we want to model mechanical sy
2
Modeling Components
Last time I mentioned that Analytical Reasoning, Computational Skills, and Physical Knowledge
are all critical components of an engineers judgment. Building those skills starts w
7
Newtons Laws with Mass
Previously, we learned about Newtons laws in Lecture 3, but in the absence of mass. Today we
are going to look at what happens when the mass at a point is nonzero. That is, we
Superposition in Vector Linear ODEs with Complex Eigenvalues
On the previous page, and in the lecture video, I talk about superposition of solutions to ODEs
when the eigenvalues are real-valued, but I
What Does The Word Linear Mean for Ordinary Differential
Equations?
At the end of Lecture 5, I talked about linearity in the context of algebraic equations. What should
linearity mean in the context o
6
Superposition
Why do we bother being so careful to design systems to have constitutive laws that are linear?
It is a reasonable question, particularly considering that we just learned in Lecture 4 t
4
Euler Integration
Last time we learned that Newtons second law leads to a differential equation. If we have a
differential equation, how should we numerically approximate its solution?
To answer thi
1
Everything Is The Same
Welcome to my Coursera class Everything is the Same: Modeling Engineered Systems. I hope you
are looking forward to the class!1
One of the most fundamental goals of this class
Wiki - Week 8 Demonstration Preparation | Coursera
https:/class.coursera.org/modelsystems-002/wiki/view?page=w.
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We
State Choices and Sign Conventions
Something that can be very annoying about all of this is how arbitrary the state choices and sign
conventions seem. Let me discuss rst what it means to have a sign c
Everything is the Same: Modeling Engineered Systems MATLAB Tutorial
If you are uncertain how to complete any of the following exercises, be sure to consult the Technical
Resources tab on Coursera to f
Diusion Instructions
As we have discussed in class, diusion of a chemical in a solution is governed
by what is called the diusion equation. The form of the equation for a system
that is not reacting i
8
Newtons Laws with Several Masses
Last time we learned that Newtons laws with mass lead to second-order ODEs that we convert
into rst-order ODEs with multiple equations. What if we want to go backwar
Why We Use Exponential Solutions
A very reasonable question that comes up is what is so special about ert ? Why not use a different
number than e, like 2.5 or or something else? And why an exponential
12
Vector Solutions to Ordinary Differential Equations
Last time we learned that vector and matrix representations can make your life easier, specically
when you implement Euler integration for a comp
21
Vector and Matrix Representations in Kirchhoffs Laws
Last time we saw that electrical systems have the same basic characteristic behavior as mechanical
systemsthey have exponential solutions and, w
23
Interpretation of Mathematical Expressions as Physical Systems
Last time we talked about analogies between physical systems. Today we are going to talk about
using physical systems to understand an
S p r in g S im u la t o r N o t e s & C h a n g e s
E v e r y t h in g is t h e S a m e
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T h
a n d m
to p o f
w ill b e
is
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th
u
s im u la t o r p r
e l p a ra m e te
e c o d e . T h e
n c o v e
24
Everything Is The SameAlmost
We are going to end with what I promised you at the beginning of the classthat everything is
the same. Well, at least with all the caveats that the system is engineered
MATLAB Tutorial Solutions
MATLAB Variables:
A1. 1 and 2
MATLAB Mathematical Functions:
A1. iii
A2. x = atan(3.14)
MATLAB as a Calculator:
A1.
s = 0.5; m = 1; x = 1.2
y = (exp(-(x-m)^2/(2*s^2)
System Identication Demonstration
Everything is the Same: Week 3
Introduction
In this demo we will show you how to identify and compute parameters for a given system. This particular
demo will consist
18
Modeling Electrical Components
Near the beginning of this course we talked about how we build models of mechanical systems
from models of mechanical components. The same thing is true of electrical
19
Kirchhoffs Laws
Last time we introduced electrical systemsvoltage, charge, current, and the constitutive laws that
relate them. What principles do we use to generate mathematical models of electric