Oscillations
Periodic and oscillatory motions
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Periodic motion: A motion which repeats itself after a fixed interval of time
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Examples:
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Motion of the moon around the earth
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Motion of the hands of a clock
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Oscillatory motion: A body in oscillatory motion moves to and fro about its mean position in a fixed time interval.
Examples:
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Motion of the pendulum of a wall clock
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Motion of the liquid contained in a U-tube when one of its limbs is compressed.
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Period (T): It is the interval of time after which a motion is repeated. Its unit is seconds (s).
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Frequency (ν): Number of repetitions that occur per unit time
Its unit is (second)-1 or Hertz.
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Displacement: Change in position
The figure shows a block attached to a spring.
Here, displacement is x.
An oscillating simple pendulum’s angular displacement isβ.
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Displacement variable may take negative values.
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Periodic functions can be expressed as a superposition of the sine and cosine functions.
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Oscillations of a block of mass, m fixed to a spring, which is in turn fixed to a rigid wall, are shown in the figure.
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The block is pulled and released so that it executes to and fro motion (SHM).
Here,
m = Mass of the block
+A, −A = Maximum displacement
(x = 0) = Position of the centre of the block at the equilibrium of the spring
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When the block is pushed to the right side, one spring is compressed while the other is elongated hence the block is subjected to a restoring force of F (x), which is proportional to the displacement, x (in the opposite direction).
As the block feels twice of restoring force because of two spring system,
∴ F (x) = −2kx …(i) Where k is the spring constant (depeā¦
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