Problems
Chapter 1
Problem 1
Problem 2
A machine of mass 500 kg is mounted on a simply
supported steel beam of length 2m having a rectangular
cross section (depth 0.1 m and width 1.2 m) and Youngs
modulus E=2.06x109 N/m2. To reduce the vertical
deflectio

Two Degrees of Freedom System
Introduction
System requiring two independent
coordinates to describe their motion are
called two degrees of freedom system.
k1
m, J0
k1
m
k2
k2
Equation of Motion
Consider a TDOF system as shown
We want to write the equat

Solutions for Spring-Mass-Damper
Systems : Forced Vibration
Single Degree of Freedom System
Harmonically excited vibration (SDOF
systems)
Whenever external energy is supplied to the
vibratory system, it is said to undergo forced
vibration
The nature can

Single Degree of Freedom (SDOF)
Systems
Mechanical Vibrations
The Spring Mass System
The Spring Mass System
We will use x
and q both as
per our
convenience
The Spring Mass System
The Spring Mass System (Damper)
The Spring Mass System (Damper)
The Spri

Mechanical Engineering Department, HITEC University, Taxila
Sessional Exam-II, ME 800, Advanced Mechanical Vibrations, Spring 2016
Time Allowed 180 Minutes
Total Points 100
INSTRUCTIONS
It is an CLOSED BOOKS, CLOSED NOTES exam, however, you are allowed on

Advanced Mechanical
Vibrations
AE 800
We will study
Introduction
Single Degree of Freedom (SDOF) Systems
Undamped and damped
Free and forced vibration
Two degrees of freedom (TDOF) Systems
Undamped and damped
Free and forced Vibration
Vibration ab

Vibration Measurement
Introduction
The theoretically vibration characteristics of
machines / structures may be different from actual,
thus there is need to measure those
The measurement of the natural frequencies of a
structure or machine is useful in s

Vibration Control and
Isolation
Introduction
There are many industrial processes which produce
vibrations
Machines or processes causing impact
Rotating machines / motors etc
Reciprocating engines
Rotating Shafts
Transporting vehicles
The presence of vib

Problems
Chapter 2
Problem 1 ~ 3
An industrial press is mounted on a rubber pad to isolate it
fro the foundation. If the rubber pad is compressed 5 m by
the self weight of the press, find he natural frequency of the
system.
A helical spring, when fixed

Solutions for Spring-Mass-Damper
Systems : General Force Conditions
Single Degree of Freedom System
General Forcing Conditions
If the forcing function is periodic, it can be
replaced with sum of harmonic functions
One equation will be replaced with many

For the figure below m2 is displaced downwards by 10 cm at t=0s and a force f=10cos20t is applied at
m3. Find the displacement of m1 at t=15s
Stifness of a rod at an angle is given by (L=cos() and m=sin() being the angle at which rod is placed)
le= rod le