Amplitude Of Simple Harmonic Motion
Simple harmonic motion is the motion of a body when it moves in a straight line path
to and fro about a fixed point, with constant amplitude and single frequency.
In other words, simple harmonic motion is a type of oscillatory motion that can be expressed in terms on a single harmonic function, or a sine or cosine curve, having a single frequency and constant amplitude.
A particle is said to execute simple harmonic motion if it moves to and fro about a mean position under the action of a restoring force .and restoring force is directly proportional to its displacement from the mean position and is always directed towards the mean position. For example: oscillations of a loaded spring, vibrations of a tuning fork and oscillations of a freely suspended magnet in a uniform magnetic field. As any object executes the simple harmonic motion it has two types of energies one is kinetic energy other is potential energy.
" A body is said to be in simple harmonic motion, if it moves to and fro along a straight line, about its mean position such that, at any point its acceleration is directly proportional to its displacement in magnitude but opposite in direction and is directed always towards the mean position".
Spin of earth on its axis is known as rotation and this fact cause Day and Night to happen in half of the earth divided equally. Because of this rotation, the Earth's surface moves at the equator at a speed of about 467 m per second or slightly over 1675 km per hour. One rotation takes almost twenty-four hours and is called a mean solar day. At any one moment of time, half of the Earth is lit by sun, while the other half is in darkness and all the credit goes to rotation which is actually good for life existence. The virtual line which divides the daylight from night is called the circle of illumination.
Examples:
Motion of the pendulum of a wall clock
Vertical and horizontal motion of a mass attached to a spring when the spring is displaced
Vibratory motion of a tuning fork when struck hard on a surface
Motion of a bar magnet suspended freely under gravity until it attains the North-South position
Motion of a liquid contained in a U tube
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Amplitude of Simple Harmonic Motion and its Derivation
The amplitude of simple harmonic motion is the displacement of the object in simple harmonic motion from its equilibrium position to its extreme position
The amplitude will be the same when measured from each extreme position, since in simple harmonic motion, the extreme positions of an object are equidistant from the equilibrium position.
Further, the amplitude of simple harmonic motion will always remain constant throughout the motion of the object if no opposing forces (such as friction) restrict the motion of the object.
By the above property of simple harmonic motions it can be expressed in the form of a simple sine or cosine curve when a displacement-time graph is drawn for it.
Derivation of amplitude formula
Since simple harmonic motion can be directly expressed as a simple sine or cosine function, we have the following formula for the displacement of simple harmonic motion at any time interval 't' seconds,
'y = a sin w t', where
y is the displacement
a is the amplitude
w is the angular frequency, and
t is the time at which displacement is measured
Thus, for amplitude the formula will be, 'a = y/(sin w t)'.
by: nitinp
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