Tag: free, forced and damped oscillations

Questions Related to free, forced and damped oscillations

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

Show answer
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.

Show answer
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.

The oscillations about a systems equilibrium position that occur in the absence of an external excitation are 

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

  1. free vibrations

  2. damped vibrations

  3. natural vibrations

  4. None of these

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Correct Option: A,C
Explanation:

The oscillations about a system of equilibrium position that occur in the absence of an external excitation are free vibrations or natural vibrations.

A person drives the paddle ball by moving his finger up and down at a certain frequency. In this example he is causing

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

  1. a damped vibration

  2. a forced vibration

  3. a mechanical vibration

  4. a transnational vinration

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Correct Option: B
Explanation:

A person drives the paddle ball by moving his finger up and down at a accelerating frequency. This is the example of force vibration as the motion of finger force to move paddle balls.

Which of the following is/are examples of forced oscillation?

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

  1. Tuning a radio

  2. Pipe instrument

  3. Rotating machinery

  4. All of the above

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Correct Option: D
Explanation:

(i) Tuning of Radio (ii) Pipe instrument (iii) Rotating machinery.

In all of the above cases system is exerted by an external force which causes its motion. So, are forced oscillation.

A driven oscillator is acted upon by a force $F={ F } _{ 0 }sin\ \omega $. The amplitude of oscillation is given by $A=\frac { { F } _{ 0 } }{ \sqrt { a{ \omega  }^{ 2\  }  -b\omega \ +c }} $, the resonant angular frequency is

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

  1. $d\frac { a }{ b }$

  2. $\dfrac { 2a }{ b } $

  3. $\dfrac { b }{a } $

  4. $\dfrac { b }{ 2a } $

Show answer
Correct Option: D
Explanation:

The driven force $ F= {F} _{0} \sin \omega t$

The amplitude of oscillation 
$A=\dfrac { { F } _{ 0 } }{ \sqrt { { a\omega  }^{ 2 }-b\omega +c }  } $
At resonance frequency A become maximum.So,
$\dfrac { dA }{ d\omega  } =0\ \Rightarrow { F } _{ 0 }\left( \dfrac { 2a\omega -b }{ \left( a{ \omega  }^{ 2 }-b\omega +1 \right)^{ \dfrac { 3 }{ 2 }}  }  \right) =0\ \Rightarrow \omega =\dfrac{b}{2a} \rightarrow$  
This is the resonence frequency.