Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
_ D8961 Course Outline
1. MATLAB tutorial
. * You are here!
1. Motion of systems that can b ' ‘ : ‘ i — particles
Description of motion; Newton’ s lavvs;
 Calculating forces required to induce prescribed motion;
 Deriving and solving equations of mo
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘page1‘—————‘ (jourms()utﬁne
l. NIATLAB tutorial
2. Motion of systems that can be idealized as particles Yﬂu are ham!
' Description of motion; Newton’s laws;
 Calculating forces required to induce prescribed I otion;
 Deriving and solving equations of
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘pagez
60:3. r A
= x154 +V
_page2 _ page 3 2 f a}: I a
z.
_ page 4 _ page 5 Given information:
 Total length L: 912 it,
 V1=125 wi‘ymin
 V2=4OO wi‘Umin
 Time t1 W 10 sec (from movie}
2.
Ea 19?; :' L“ ZZ 7" Zr— ! r L
. . 25 J": 3’ 1 E I
1:; 2
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘page 1 — Course Outline
1. MATLAB tutorial
You are here!
2. Motion of systems that can be idealized as particles
' Description of motion; Newton’s laws;
 Calculating forces required to induce prescribed motion;
 Deriving and solving equations of motion
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
_ page 1
_ page 1
Course Outline
1. MATLAB tutorial
2. Forces (selfstudy on notes)
3. Motion of systems that can be idealized as particles
 Description of motion; Newton’s laws; Calculating forces required
to induce prescribed motion; Deriving and sol
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
 page 1 — Course Outline
1. MATLAB tutorial
2. Motion of systems that can be idealized as particles
' Description of motion; Newton’s laws; You a 113 here!
 Calculating forces required to induce prescribed motion;
' Deriving and solving equations of m
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘page 1 —
_ page 1
l.
to
[A
Course Outline
NlA'IlAB tutorial
Motion of systems that can he idealized as particles
Conservation laws for systems of particles
Description of motion; Newtonislaws;
Calculating forces required to induce prescribed motion;
De
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘Page‘ Course Outline
1. MATLAB tutorial
2. Forces (selfstudy on notes)
3. Motion of systems that can be idealized as particles
 Description of motion; Newton’s laws; Calculating forces required
to induce prescribed motion; Deriving and solving equation
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘page i —
_ page i
1
Course Outline
MATLAB tutorial
Motion of systems that can be idealized as particles
. . . You are here!
Description of motion; Newton's laws;
Calculating forces required to induce prescr' "‘i motion;
Deriving and solving equati
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
_ page1— Course Outline
1. MATLAB tutorial
2. Motion of systems that can be idealized as particles
 Description of motion; Newton’s lavvs;
 Calculating forces required to induce prescribed motion;
 Deriving and solving equations of motion
3. Conserva
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Rigid Bodies
PARTICLES: no rotation, just translation
RIGID BODIES: arbitrary shaped bodies that do not
deform  must consider translation and rotation
Rigid Body Motion
Kinematics  describes motion (position, vel,
accel) without regard for the forces
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Rigid Body Kinematics
vA = vB + (! rA/B )
aA = aB + ( rA/B ) + (! (! rA/B )
Useful Shortcuts for 2D planar motion = k
! = !k
r = r x i + ry j
!r =
r =
! (! r) =
ry !i + rx !j
ry i + rx j
rx ! i
2
ry ! j
2
rigid body dynamics problems:
2D planar motion
Fr
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
— page 1 — Course Outline
1. MATLAB tutorial
2. Motion of systems that can be idealized as particles
' Description of motion; Newton’s laws;
* Calculating forces required to induce prescribed motion;
 Deriving and solving equations of motion
3. Conserv
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Rolling Disk (no slip)
O
C
C
Motion of Center (O):
s = R
vo=R
ao=R
O
C
O
Rcos
Rsin
Motion of Point C:
x = sRsin = R(sin)
vcx= R(1cos)
acx=R(1cos)+ R2(sin)
y = R(1cos)
vcy= R(sin)
acy=R(sin)+ R2(cos)
Rolling Disk (no slip)
B
B
O
C
O
C
rB = rO + rB/O
v
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
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Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
EN40: Dynamics and Vibrations
Division of Engineering
Brown University
Solutions to Differential Equations of Motion for Vibrating Systems
Here, we summarize the solutions to the most important differential equations of motion that we
encounter when analy
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
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Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
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Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
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Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Untitled 8.pdf
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Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
_ page 1 — Course Outline
1 MAI—LAB tutorial
2. Motion of systems thaI can be idealized as parﬁcles
' Description of motion; Newton‘slaws;
 Calculating forces required to inctuce prescribed motion;
 Deriving and solving equations of motion
3 Conserv
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Chapter 3
Analyzing motion of systems of particles
In this chapter, we shall discuss
1. The concept of a particle
2. Position/velocity/acceleration relations for a particle
3. Newtons laws of motion for a particle
4. How to use Newtons laws to calculate t
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Chapter 2
Review of Forces and Moments
2.1 Forces
In this chapter we review the basic concepts of forces, and force laws. Most of this material is identical
to material covered in EN030, and is provided here as a review. There are a few additional section
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
‘ page 1 — Course Outline
1. MATLAB tutorial
2. Motion of systems that can be idealized as particles
* Description of motion; Newton‘s laws;
 Calculating forces required to induce prescribed motion;
* Deriving and solving equations of motion
3. Conserv
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
mag“ Solar Car Project
 Goal: design and constructa small solar powered vehicle that
will climb a ramp at max possible speed.
 Approach: Select transmission ratio (gears, wheel radius) that
will extract max power from solar panels and motor.
Construct
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Chapter 5
Vibrations
5.1 Overview of Vibrations
5.1.1 Examples of practical vibration problems
Vibration is a continuous cyclic motion of a structure or a component.
Generally, engineers try to avoid vibrations, because vibrations have a number of unpleas
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
Chapter 4
Conservation laws for systems of particles
In this chapter, we shall introduce (but not in this order) the following general concepts:
1. The linear impulse of a force
2. The angular impulse of a force
3. The power transmitted by a force
4. The
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
EN40: Dynamics and Vibrations
Midterm Examination
Tuesday March 5 2013
School of Engineering
Brown University
NAME:
General Instructions
No collaboration of any kind is permitted on this examination.
You may bring 2 double sided pages of reference notes.
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
EN40: Dynamics and Vibrations
Final Examination
Tuesday May 15, 2011
School of Engineering
Brown University
NAME:
General Instructions
No collaboration of any kind is permitted on this examination.
You may use 2 double sided pages of reference notes. No o
Birla Institute of Technology & Science, Pilani  Hyderabad
Dynamics
MECH 879

Spring 2014
EN40: Dynamics and Vibrations
Midterm Examination
Tuesday March 9 2010
Division of Engineering
Brown University
NAME:
General Instructions
No collaboration of any kind is permitted on this examination.
You may bring 2 double sided pages of reference notes