Physics - Oscillations

Oscillations
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Periodic Motion

Any object that moves to-and-fro
repeatedly is said to execute
periodic motion.
Note:
But NOT all periodic motions are
necessarily Simple Harmonic Motions
(SHM).

An example of a
Simple Harmonic Motion



• A simple
pendulum
swinging with a
small angular
displacement.


What constitute a SHM?


A special kind of periodic motion occurs in
mechanical systems when the (net) force
acting on an object is proportional to the
position of the object relative to some
equilibrium position.
And, if this force is always directed toward
the equilibrium position, the motion is called
position
simple harmonic motion.


How can you
recognise
Simple
Harmonic
Motion from a

displacement
-time graph?


The variation of the vertical displacement
of the oscillator with time.

Simple Harmonic Motion is one whose
displacement-time graph is like a sine curve
(A sinusoidal graph).
It is called ‘simple’ because it is the most
fundamental of any periodic motion.

Periodic Motion - SHM

A tuning fork prong


Periodic Motion - SHM

Watch Balance Wheel


Objects that are NOT describing
SHM in the following slides


Periodic Motion

Cone of loudspeaker

An example of periodic motion
that is NOT SHM

Periodic Motion

Body of guitar

that is NOT SHM

Periodic Motion

Piston
in engine

that is NOT SHM

More examples of periodic
motions that are NOT SHM

s

Pulse of the heart beating
A ball bouncing up and
down the floor.

• Vibrations of a guitar string.
• Vibrations from an
earthquake.

Example of SHM

• A simple
pendulum
swinging with a
small angular
displacement.
Provided the angular
displacement is small.,
it is SHM.

Example of SHM
• A loaded spring
oscillating about
an equilibrium
position.
It is SHM as long as
Hooke’s law is
obeyed.

Examples of SHM

• The prongs of a
tuning fork
vibrating.

• A floating test-
tube oscillating
vertically on the
water surface.


Free Oscillations that are
SHM
There is no resistive force such as friction, air
resistance and fluid resistance acting on the
system.
Its amplitude remains constant with time and
no energy is lost to the surroundings.
The total mechanical energy of the system
undergoing SHM is conserved.
Such oscillations are called free oscillations.

SHM

Simple Pendulum Mass attached
to centre of
elastic string

SHM

Mass on frictionless surface Disc attached to torsion wire


Investigating SHM


Equation of Motion (Solution)

Depends on the initial condition for the oscillator:
x = x sin ωt (if x = 0, when t = 0 )
o

x = xo cos ωt (if x = +xo, when t = 0)

(if x is neither at the equilibrium point nor
the extreme points when t = 0)
x = xo sin(ωt + φ )

Definition of Terms
• Period T
• the time
required to
complete one
full
oscillation or
cycle of
motion.


Definition of Terms
• Frequency f
• the number of
complete
oscillations
per unit time.
1 1
f = T=
T f


Definition of Terms
• Equilibrium
Position O
• the position
at which no
net force acts
on the
oscillating
object.


Definition of Terms
• Displacement x
• the linear
displacement of
the oscillating
object from its
equilibrium
position at any
instant. It is a
vector quantity.


Definition of Terms
• Amplitude xo
• the maximum
distance of the
oscillating
object
measured from
the equilibrium
position. It is a
scalar quantity.


Definition of terms

• Angular displacement

frequency, ω amplitude

• defined as the
time
product of the
frequency of
oscillations
and 2π radian.

2π 2π
ω = 2πf ω = T=
T ω www.flipperworks.com

Angular frequency and
speed
Angular frequency angular speed
ω ω
In the context of In the context of
SHM, we refer ω circular motion is
as ‘angular defined as the rate
frequency’. change of angular
displacement.

Phase
Phase is a term used to describe
angle θ the stage of a particle in its
cycle of SHM oscillation. It
is measured in radians.
Phase is the difference in phase
difference between two oscillators
∆θ when they oscillate at the
same frequency. It is
measured in radians.

In phase

Out of phase

Example 1

Lecture Assignment 1
Using the oscillation for A as the reference, determine
which of the above oscillations is
(i) in phase with A,

(ii) anti-phase with A

(iii) out of phase with A by 90o or π/2 radian Ans: C,D,B

Physics - Oscillations

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