Simple
Harmonic Motion (SHM) is a motion in which the restoring force is inversely
correlated with the body's deviation from its mean position. This restorative
power is always directed toward the mean position. A particle's acceleration in
Simple Harmonic Motion is given by a(t) = -ω2 x(t). Here, ω is
the particle's angular velocity.
On
that note, let’s learn all important concepts related to Simple Harmonic Motion
from the definition, equation, and types to differences with other oscillatory
motions with examples in detail.
Simple Harmonic,
Periodic and Oscillation Motion
Simple
Harmonic Motion is an oscillatory motion in which the particle's acceleration
at each position is directly proportional to its displacement from the mean
position. It's a type of oscillation or oscillatory motion.
Simple
Harmonic Motions (SHM) are all oscillatory and periodic, however not all
oscillatory motions are SHM. Oscillatory motion is frequently referred to as
the harmonic motion of all oscillatory motions, the most important of which is
simple harmonic motion (SHM).
Simple
Harmonic Motion is a very useful tool for understanding the characteristics of
sound waves, light waves, and alternating currents. Any non-simple harmonic
oscillatory motion can be expressed as a superposition of several harmonic
motions of different frequencies.
Difference between
Periodic, Oscillation and Simple Harmonic Motion
Periodic Motion
● A motion repeats itself after an equal time
interval. Consider uniform circular motion.
● There is no place of equilibrium.
● No restorative force exists.
● There is no steady state of equilibrium.
Oscillation Motion
● A particle moving back and forth around a
mean position is referred to as oscillatory motion when it moves on either side
of the equilibrium or mean position.
● It is a particular type of periodic motion
that is limited by two extremes. For instance, the Spring-Mass System or the
Oscillation of a Simple Pendulum.
● The mean position (or equilibrium position)
along any path is where an object will continue to move while oscillating
between two extreme positions about a fixed point. The path itself is not a
restriction.
● The equilibrium position (or mean position)
will be the target of a restoring force.
● The net force acting on the particle in an
oscillatory motion is zero at the mean position.
● A stable equilibrium position is the mean
position.
Simple Harmonic
Motion or SHM
● Between the two extreme points, it is a
specific example of oscillation along a straight line (the path of SHM is a
constraint).
● The thing must go in a straight line.
● The equilibrium position (or mean position)
will be the target of a restoring force.
● A stable equilibrium exists at the mean
position in simple harmonic motion.
Types of Simple
Harmonic Motion
Simple
Harmonic Motion, or SHM, can be divided into two categories:
● Linear Simple Harmonic Motion
● Angular Simple Harmonic Motion
Linear Simple
Harmonic Motion
Simple
harmonic motion is referred to when a particle oscillates in a straight line
and around a fixed point (known as the equilibrium position).
Consider
a spring-mass system.
Angular Simple
Harmonic Motion
When
a system oscillates angularly far from a fixed axis, an angular simple harmonic
motion happens.
Terminology in
Simple Harmonic Motion
Mean position
The
mean position is typically defined as the position where the net or total force
on the particle in SHM is zero.
Extreme Position
An
extreme position is one that is situated at a distance equal to the amplitude
of the Simple Harmonic Motion (SHM). At an extreme position, the velocity is
typically zero and the acceleration is highest.
Amplitude
The
greatest deviation from the mean position is referred to as the amplitude.
Phase
For
a simple harmonic motion, phase is described as a quantity that falls inside
the trigonometric function for a particle's position. Phase identifies the
state of simple harmonic motion, which is its position and direction of motion.
Time Period
The
time interval after which the particle returns to its initial phase is how the
time period is defined or expressed.
Linear Frequency
Frequency
is the Inverse of the time period.