This document discusses different types of vibrations including free vibrations, forced vibrations, and forced-damped vibrations. It provides examples of each type and notes that forced vibrations can be created by step input forcing, harmonic forcing, or periodic forcing. Methods to isolate vibrations transmitted to machine foundations using springs and dampers are also covered, along with the concept of transmissibility to determine the amount of vibrations transmitted. Key equations for forced-damped vibrations and transmissibility are presented.

1. Vibrations
• Free Vibrations : Vibrations that
occur in the absence of friction
and external forces after initial
release of body.
Eg: Simple Pendulum
• Forced Vibrations : When
repeated force continuously acts
on the system the vibrations are
said to be forced vibrations.
Eg: Pendulum in a Clock

2. Forced Vibrations
• Vibrations can be created
by any following methods
of forcing.
1. Step input forcing
2. Harmonic forcing
3. Periodic forcing

3. Examples of Forced Vibrations
• Vibration of Floor caused by running
of heavy machinery.
• Vibration of car when running in an
uneven road surface.
• Vibration in reciprocating engines
due periodic reciprocating of
pistons.

4. Forced-Damped Vibrations
Given Force, F = F0sinωt ↓
Inertia Force = mẍ ↑
Damping Force = cẋ ↑
Spring Force = sx ↑
mẍ + cẋ + sx = F0sinωt
• The equation is solved using
Complementary function and Particular
integral.
• x= CF + PI

5. • Complementary function =
• Particular Integral =
• x = +
• In actual practice the value given by complementary function is so small
and is usually neglected.
• Amplitude, A =

6. Vibration Isolation
• Vibrations produced in a machine is transmitted to the
foundation upon which it is mounted. These vibrations
produce undesirable effects and should be avoided.
• These Vibrations should be isolated using Springs and
Dampers.
• The concept of Transmissibility comes into role to
determine the amount of vibrations that are
transmitted to the foundation and Isolate the same.

7. Transmissibility
• The ratio of the force transmitted (FT) to the force applied
(F) is known as the transmissibility (ɛ).
• Force Transmitted:
• Force Transmissibility :