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What do you understand by natural frequency?

Important Questions on Oscillations

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

Time period of a simple pendulum is

T

inside a lift when the lift is stationary. If the lift moves upwards with an acceleration

\frac{g}{2}

, the time period of pendulum will be :

HARD

Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

A simple harmonic oscillator of angular frequency

2 rad s^{- 1}

is acted upon by an external force

F = \sin t N .

If the oscillator is at rest in its equilibrium position at

t = 0,

its position at later times is proportional to:

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

In an experiment to determine the gravitational acceleration

g

of a place with the help of a simple pendulum, the measured time period squared is plotted against the string length of the pendulum in the figure. What is the value of

g

at the place?

HARD

Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

The path length of oscillation of simple pendulum of length

1 m

16 cm

. Its maximum velocity is

(g = π^{2} {m s}^{-2})

HARD

Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulum is

MEDIUM

Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

In an experiment to determine the period of a simple pendulum of length

1 m

, it is attached to different spherical bobs of radii

r_{1}

and

r_{2}

. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be

5 \times 10^{- 4} s

, the difference in radii,

|r_{1} - r_{2}|

is best-given by

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

Two pendulums $C$ and $D$ are suspended from a wire as shown in the given figure. Pendulum $C$ is made to oscillate by displacing it from its mean position. It is seen that $D$ also starts oscillating. Name the type of oscillation, $D$ will execute.

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

A vibration tuning fork is placed over the mouth of a burette filled with water. The tap is opened and the water level gradually falls. It is observed that the sound becomes the loudest for a particular length of air column.

Why does the sound become the loudest?

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force.

F = F_{0} \sin ω t

If the amplitude of the particle is maximum for

ω = ω_{1}

and the energy of the particle is maximum for

ω = ω_{2}

then

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

Distinguish between free and forced vibration.

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

Two springs of force constants

K_{1}

and

K_{2}

, respectively, are connected to a mass

m

, as shown. The frequency of oscillation of the mass is

f

. If both

K_{1}

and

K_{2}

are made four times their original values, the frequency of oscillation becomes

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

In case of a forced vibration, the resonance peak becomes very sharp when the

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

How does the free vibration depend on the frequency?

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

What are free and forced vibrations? Give one example of each.

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

A particle of mass

m

is attached to a spring (of spring constant

k

) and has a natural angular frequency

ω_{0} - A n

external force

F (t)

proportional to

c o s ω t (ω \neq ω_{0})

is applied to the oscillator. The time displacement of the oscillator will be proportional to

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

The force acting on a particle moving along

x

-axis is,

F = - k (x - v_{0} t)

where,

k

is a positive constant. An observer moving at a constant velocity

v_{0}

along the

x

-axis looks at the particle. What kind of motion does he find for the particle?

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

When a body of natural frequency

n

is subjected to the external force vibrating with frequency

p

, the body vibrates with frequency

p

under steady state with an amplitude which depends upon

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

On what factors does the natural frequency of a body depend?

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

Represent the union of two sets by Venn diagram for each of the following.

$X = {x | x$ is a prime number between $80$ and $100}$

$Y = {y | y$ is an odd number between $90$ and $100}$

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Physics>Advanced Mechanics>Oscillations>Free and Forced Oscillations

State condition for a body to execute free vibrations.

What do you understand by natural frequency?

Important Questions on Oscillations

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