EGR 244 Dynamics Spring 2015 Semester Prof. Benjamin B Yellen
Homework Instructions
A problem solution is a form of technical communication and should therefore be very
clear and easy to understand. The computer is a tool and should only be used after the

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I asked Pat to print several blocks. We did this test
and obtained \beta=15 degrees. Convert \beta to radians
by multiplying by \pi/180 before trying to find \mu_s.

Course Notes by Brian Mann, Duke University
1
Lagranges Equations
1
Introduction
Deriving the equations of motion is often the rst step in a more detailed study of a physical
system. This document develops a theoretical basis for the derivation of the equ

Duke University
Pratt Schook of Engineering
EGR123 Dynamics
1. Consider a cube with sides of length 4? and uniform density ,0. If the mass moments of
inertia about axes through the mass center are 1W = IW m [mm m $47122, nd Im and
any four products of i

Course Notes by Brian Mann, Duke University
1
1
Single Particle Angular Momentum
The angular momentum vector Ho about the point o is given by
Ho = ri mi vi
(1)
where ri a position vector to the mass mi and vi is a velocity vector of the mass. The sum of t

Duke University
EGR244 Pratt School of Engineering Dynamics
Pratt School of Engineering
EGR 244: Dynamics
Exam 1
February 18, 2015
Name: Lo Sh. anchor Solve
Upon my honor I pledge that I have neither given nor received aid related to this examination.
S

Duke University
Pratt School of Engineering Dynamics
EGR244
1. Consider the foilowing two dierential equations beiow which describe two identical
pendulumS. Derive expressions for the rst two natural frequencies of this coupled
system in terms of ,u and

Course Notes by Brian Mann, Duke University
1
Work and Energy
1
Work of external forces
Work is a scalar quantity that can be dened through an integral equation,
r(t2 )
W=
t2
F(r) dr =
r(t1 )
F(r) rdt ,
(1)
t1
where F(r) is the force along the path r duri

EGR244: Dynamics
Dr. Brian Mann
MEMS Department
Duke University
2015
(Duke University)
Dynamics
2015
1/9
Angular Momentum from Many Particles in a Bigid Body
Rigid Body - no deformation
Angular Momentum n-particles
n
ri/c mi vi/c
Hc =
i=1
ri/c = xi u1 + y