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Chapter 13 Oscillations
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Chapter 13 Oscillations
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Oscillations
Non Periodic Motion
The motion which is non-repetitive .
e.g. rectilinear motion , motion of a projectile.
Periodic Motion
A motion that repeats itself at regular intervals of time is called periodic
motion.
e.g. uniform circular motion , orbital motion of planets in the solar system.
Oscillatory Motion
Periodic to and fro motion is called oscillatory motion.
e.g. motion of a cradle , motion of a swing, motion of the pendulum of a
wall clock.
Every oscillatory motion is periodic, but every periodic motion need not
be oscillatory.
Oscillations and Vibration
There is no significant difference between oscillations and vibrations.
▪ When the frequency is small, we call it oscillation.
e.g.The oscillation of a branch of a tree
▪ When the frequency is high, we call it vibration.
e.g. The vibration of a string of a musical instrument.
Period and frequency
Period (T)
The period T is the time required for one complete oscillation, or cycle.
Its SI unit is second.
Frequency
The frequency ν of periodic or oscillatory motion is the number of
oscillations per unit time.
It is the reciprocal of period .
𝟏
𝛎=
𝐓
The SI unit of ν is hertz ( Hz).
(In honor of the discoverer of radio waves, Heinrich Rudolph Hertz)
1Hz =1oscillation per second =1s−1
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Example
On an average a human heart is found to beat 75 times in a minute.
Calculate its frequency and period.
75
The beat frequency of heart , ν =
1min
75
=
60 s
= 1.25 s−1 = 1.25 Hz
1
The time period ,T =
1.25
T = 0.8 s
Displacement
The distance from mean position is called displacement ( x)
At mean position displacement x= 0 and at extreme position x= ±𝑨
A is called amplitude of oscillation.
Amplitude
The maximum displacement from the mean poition is called amplitude
(A) of oscillation.
Mathematical Expression for Displacement
The displacement can be represented by a mathematical function of time.
It can be a sine function, cosine function or a linear combination of sine
and cosine functions.
f (t) = A cos ωt or
f (t ) = A sin ωt.
f (t) = A sin ωt + B cos ωt
Where A = Amplitude
ω=angular frequency
𝟐𝛑
ω= or ω= 𝟐𝛑𝛎
𝐓
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