Tag: oscillation and waves

Questions Related to oscillation and waves

A wire stretched between two fixed supports, is plucked exactly in the middle and then released. It executes (neglect the resistance of the medium) :

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. resonant vibrations

  2. free vibrations

  3. damped vibrations

  4. forced vibrations

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Correct Option: B
Explanation:

A wire stretched between two fixed supports, is plucked exactly in the middle and then released. It executes free vibrations.
Free vibrations are oscillations where the total energy stays the same over time. This means that the amplitude of the vibration stays the same. This is a theoretical idea because in real systems the energy is dissipated to the surroundings over time and the amplitude decays away to zero. This dissipation of energy is called damping.

A transverse wave is passing through a medium. The maximum speed of the vibrating particle occurs when the displacement of the particle from the mean position is

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. zero

  2. half of the amplitude

  3. equal to the amplitude

  4. none of the above

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Correct Option: A
Explanation:

The maximum speed of the vibrating particle is when particle is on mean position.
In general total energy of the system remains constant. At the mean position potential energy is minimum this implies that kinetic energy will be maximum. Hence speed will be maximum. 

The vibrations of a body which take place under the influence of an external periodic force acting on it are called 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. Forced vibrations

  2. Free vibration

  3. Damped vibrations

  4. All

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Correct Option: A
Explanation:

Forced vibrations: External force is acting on the body. 
Free vibration: Constant amplitude and no external force.
Damped vibration: Amplitude is not constant, it keeps on decreasing due to environmental factors of the system like air resistance.  
Therefore, correct option is A. 

A simple pendulum of length 4 m is taken to a height $R$ (radius of the earth) from the earth's surface.The time period of small oscillations of the pendulum is $(g _{surface}={\pi}^{2 } m{s}^{-2})$

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. 2 s

  2. 4 s

  3. 8 s

  4. 16 s

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Correct Option: C
Explanation:

The acceleration due to gravity of earth at a high 'h' 

${g} _{h} = {g} _{surface}\left( 1+\dfrac { h }{ R }  \right) ^{ -2 }$
g = acceleration due to surface gravity at earth surface
Now h = R (given)
so, ${g} _{h} = \dfrac { { g } _{ surface } }{ 4 } $
Now the time period of simple pendulum of length 4m at earth surface is 
${ T } _{ surface }=2\pi \sqrt { \dfrac { l }{ { g } _{ surface } }  } =2\pi \sqrt { \dfrac { 4 }{ 9.8 }  } \approx 4sec$
So time period at hight 'h = 2R' is 
$T=2\pi \sqrt { \dfrac { l }{ g _h }  } =2\pi \sqrt { \dfrac { 4\times 4 }{ { g } _{ surface } }  } =8sec$

A wave is measured to have a frequency of $60 Hz$. If its wavelength is $24 cm$, determine how fast it is moving.

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. $24 m/s$

  2. $10 m/s$

  3. $12 m/s$

  4. $14 m/s$

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Correct Option: D
Explanation:

We know $ v = n \times \lambda  $

$v= 60 \times 24 \times 10^{-2}$
$v=14.4 m/s$

The oscillations of a pendulum about a vertical equilibrium position is an example of

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. damped vibration

  2. free vibration

  3. forced vibration

  4. random vibration

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Correct Option: B
Explanation:

The oscillation of a pendulum about a vertical equilibrium position is an example of free vibration. As there no exciting force is present.

Which of the following is/are correct?

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. The vibration of drilling machine depends on a force from outside

  2. The vibration of drilling machine does not depend on a force from outside

  3. When a pendulum vibrates it is free vibration because it does not depend on any outside force to vibrate

  4. When a pendulum vibrates it is free vibration because it depends on any outside force to vibrate

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Correct Option: A,C
Explanation:

The correct statements are:

$A$ The vibration of drilling machine depends on the force from outside. Here the driven machine is driven by electricity.
$C$ When a pendulum vibrate it is free vibration because it does not depend upon any outside force to vibrate.

If ${\omega} _d$ is a frequency of a driving force, then forced oscillations can be described by which of the following?  $b=$ least damping.

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. $x(t)= A({\omega} _d/\omega , \ b) cos({\omega} _d t+ \phi)$

  2. $x(t)= A({\omega} _d/\omega , \ b) cos({\omega} _d )$

  3. $x(t) = A sin\theta + B cos\theta $

  4. $x(t) = \sqrt{A sin\theta + B cos\theta} $

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Correct Option: A

Forced oscillation is 

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. simple harmonic motion but driven externally

  2. simple harmonic motion without driven externally

  3. having resonance when the driving frequency is the same as the natural frequency of the swing.

  4. Both A and C

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Correct Option: D
Explanation:

The force oscillation is (1) a simple harmonic motion driven by an external agency 

(ii) It has a resonance when the natural frequency of motion is equal to the driven frequency. 
At resonance the amplitude of motion and velocity of motion become maximum.

Which of the following is/are the correct option(s)?

free, damped and forced oscillations free, forced and damped oscillations oscillations oscillation and waves physics

  1. A louder sound is always produced when an accompanying object of smaller surface area is forced into vibration at the same natural frequency.

  2. A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the different natural frequency.

  3. A louder sound is always produced when an accompanying object of greater surface area is forced into vibration at the same natural frequency.

  4. A louder sound is always produced when an accompanying object of smaller surface area is forced into vibration at the different natural frequency.

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Correct Option: C
Explanation:

Statement C is true, consider the case of a guitar string mounted to the sound box. The fact that the sound box is greater than the surface area of the string means more surrounding particles will be forced into vibration causes an increase in amplitude and loudness.