Texas A&M University
Department of Mechanical Engineering
MEEN 363 - Section 502 - Spring 2016
Exam 5 (Final)
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Solutions Manual
to accompany
Applied Numerical Methods
With MATLAB for Engineers and Scientists
Steven C. Chapra Tufts University
CHAPTER 1
1.1 You are given the following differential equation with the initial condition, v(t = 0) = 0,
c dv = g d v2 dt m
TEXAS A&M UNIVERSITY
Department of Mechanical Engineering
MEEN 363
Dynamics and Vibrations
FALL 2014
Homework # 5
1. Consider the motion of a mechanical system shown in the figure below. The cart has
a mass M kg and the pendulum has a mass m kg and is of
Texas A&M University
Department of Mechanical Engineering
FALL 2014
MEEN 363
Dynamics and Vibrations
Homework III
1. A rotor of mass, M , and of moment of inertia, I, about its axis of symmetry is laid
with its journals on two guides with a radius of curv
MEEN 363:
Dynamics & Vibrations
S. Darbha1
1 Department of Mechanical Engineering
Texas A & M University, College Station, TX - 77843,
Texas A&M University, Qatar.
Fall 2014
Swaroop Darbha (TAMU)
Supplementary Notes
1 / 31
Introduction
Motion of a materia
Examtle
A heavtf soll'ol cjlu‘nder‘ DJC diameﬂ B=2RJ C1170?
mass ”am Can mull over“ :1 how‘zonqul surface. w?le
blfﬂol‘ng “Two springs 0? 55}an h ”/09 Each am
attacked} 4'0 {4‘2 (135k di— 4 AJAEGHCI; e abom 1.15
cen‘rcr of mm (LE: 59mm?! 13/] “Hug Ex‘gurm
Problem 1: Consider a system with two masses m] and m2 moving on an inclined plane as
shov.'11 in the figure below. The position of the massless plate is denoted by Xb(t). There is an
external force , F(t), acting on the mass m] as shov.'TI in the figure.
Texas A&M University
Department of Mechanical Engineering
FALL 2014
MEEN 363
Dynamics and Vibrations
Homework IV
1. An automotive suspension is modeled as a spring-mass-damper system as shown in
Figure 1. The road profile is given by y(t) = A cos( 2x
L ),
Solulmj J 511.1 MN“ wovlg anrh
' 7 7mm s In '
The 4-11 slender bar weiﬂxs 40 lb with center at B ls l3:
rest in the position for which 9 is essentially zerotPoint/{BK is conﬁan moVe'in L s, g
" 3 the smooth vertical guide, while endA moves in; the L
MEEN 363 Final Exam Summary Sheet (The final is closed book and notes, no cheat sheets) c Paul Stiverson, TAMU You are
responsible for all of these equations, none of these will be provided on the exam.
1
Torsion Problems
1. Define assumed kinematics betw
c Paul Stiverson, TAMU
MEEN 363 Exam 5 Summary Sheet (Exam 5 is closed book and notes, no cheat sheets)
You are responsible for all of these equations, none of these will be provided on the exam.
1
Center of Gravity
1. Define a reference system for the a
MEEN 363
Notes # 2
1
Modeling and Response of Mechanical Systems: Overview
1
Modeling single degree of freedom systems.
Free response of a spring-mass-damper system
Forced response of a spring-mass-damper system
Transmissibilty
TAMU
MEEN 363
Darbha
No
TEXAS A&M UNIVERSITY
Department of Mechanical Engineering
MEEN 363
Dynamics and Vibrations
FALL 2014
Modes and Mode Shapes
1
Introduction
Before we proceed further with our discussion of natural frequencies and mode shapes, we
will first define Simple Har
MEEN 363
Notes # 2
1
Mechanics of Rigid Bodies - Overview
1
Rigid body - definition and degrees of freedom
Kinematics of Rigid Bodies
Kinetics of Rigid Bodies - Moment of Inertia and Newton-Euler
Equations.
TAMU
Darbha
MEEN 363
Notes # 2
2
Rigid Body
TEXAS A&M UNIVERSITY
Department of Mechanical Engineering
MEEN 363
Dynamics and Vibrations
FALL 2014
Modes and Mode Shapes
1
Introduction
Before we proceed further with our discussion of natural frequencies and mode shapes, we
will first define Simple Har
Texas A&M University
Department of Mechanical Engineering
FALL 2014
MEEN 363
Dynamics and Vibrations
Homework II
1. In the figure shown below, ABCD is a smooth, frictionless track containing, two
straight sections, AB and CD, and a curved section, BC of r