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Simple Harmonic Motion Guide

A Simple Harmonic Motion, or SHM, is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position. The acceleration of a particle executing simple harmonic motion is given by a(t) = -ω2 x(t). Here, ω is the angular velocity of the particle.

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81 views18 pages

Simple Harmonic Motion Guide

A Simple Harmonic Motion, or SHM, is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position. The acceleration of a particle executing simple harmonic motion is given by a(t) = -ω2 x(t). Here, ω is the angular velocity of the particle.

Uploaded by

M Shafeeq Manzoor
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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Simple Harmonic Motion

 Definition
 Formula's
 Applications
CONTENTS

 Periodic Motion
 Time Period
 Frequency
 Displacement
 Restoring Force
Periodic Motion

It Is A Motion That Is Repeated In Equal Intervals


Of Time.

Examples:
A Rocking Chair, A Bouncing
Ball, A Vibrating Tuning Fork, A
Swing In Motion, The Earth In Its
Orbit Around The Sun, And A
Water Wave.
Displacement
The displacement of a vibrating body is the distance
from its mean position. The maximum displacement is
called the amplitude
Time Period

The period of time it takes to get back to where it


started is called time period.

 It is denoted by (T).
 Time is inversely proportional to frequency.
 The SI unit of time period is Second.
 The unit of time period is denoted by ‘s’.
Time Period
Formula:
Frequency

The number of complete cycles each second is called


Frequency.

 It is denoted by (f).
 Frequency is inversely proportional to time.
 The SI unit of frequency is Hertz.
 The unit of frequency is denoted by ‘Hz’.
Frequency
Formula:

f
Restoring Force
The force that always points back to the equilibrium
position is Restoring Force.
Restoring Force
According to Hook’s Law:
The force is needed to compress or extend a spring is
directly proportional to the distance you stretch it.
Equation:
Fr=-kx
 F is the force we apply.
 K is the spring constant.
 X is the extension of spring material.
Simple Harmonic Motion
Definition:-
A body is undergoing SHM when the acceleration on the
body is proportional to its displacement, but acts in the
opposite direction.
Explanation
Consider a mass "m" attached to the end of an elastic spring as shown in figure "a". If
we displace the mass 'm' from its mean position 'O' to point "a“.
it is displaced by '+x' to its right, there will be elastic restoring force on the mass
equal to F in the left side
According to "Hook's Law

F = kx ---- (1)
If we release mass 'm'
it moves forward to ' O'. At point ' O' it will not stop but
moves forward towards point "b" due to inertia and
covers the same displacement -x. At point 'b' once again
elastic restoring force 'F' acts upon it but now in the right
side. In this way it continues its motion
 from a to b and then b to a.
According to Newton's 2nd law of motion, force 'F' produces
acceleration 'a' in the body which is given by
F = ma ---- (2)
Comparing equation (1) & (2)
ma = -kx

Here k/m is constant term, therefore ,


a = - (Constant)x
or

This relation indicates that the acceleration of body attached to the


end elastic spring is directly proportional to its displacement.
Therefore its motion is Simple Harmonic Motion.
Applications of SHM
 Car Shock Absorbers
 Musical Instruments
 Bungee Jumping
 Diving Board
 The Process of Hearing
Car Shock Musical Instruments
Absorbers
Bungee Jumping The Process of Hearing
Diving Board

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